diff --git a/app/code/Magento/QuoteGraphQl/Model/Cart/Address/AddressDataProvider.php b/app/code/Magento/QuoteGraphQl/Model/Cart/Address/AddressDataProvider.php
new file mode 100644
index 000000000000..fb742477ec99
--- /dev/null
+++ b/app/code/Magento/QuoteGraphQl/Model/Cart/Address/AddressDataProvider.php
@@ -0,0 +1,94 @@
+<?php
+/**
+ * Copyright © Magento, Inc. All rights reserved.
+ * See COPYING.txt for license details.
+ */
+declare(strict_types=1);
+
+namespace Magento\QuoteGraphQl\Model\Cart\Address;
+
+use Magento\Framework\Api\ExtensibleDataObjectConverter;
+use Magento\Quote\Api\Data\AddressInterface;
+use Magento\Quote\Api\Data\CartInterface;
+use Magento\Quote\Model\Quote\Address as QuoteAddress;
+
+/**
+ * Class AddressDataProvider
+ *
+ * Collect and return information about cart shipping and billing addresses
+ */
+class AddressDataProvider
+{
+    /**
+     * @var ExtensibleDataObjectConverter
+     */
+    private $dataObjectConverter;
+
+    /**
+     * AddressDataProvider constructor.
+     *
+     * @param ExtensibleDataObjectConverter $dataObjectConverter
+     */
+    public function __construct(
+        ExtensibleDataObjectConverter $dataObjectConverter
+    ) {
+        $this->dataObjectConverter = $dataObjectConverter;
+    }
+
+    /**
+     * Collect and return information about shipping and billing addresses
+     *
+     * @param CartInterface $cart
+     * @return array
+     */
+    public function getCartAddresses(CartInterface $cart): array
+    {
+        $addressData = [];
+        $shippingAddress = $cart->getShippingAddress();
+        $billingAddress = $cart->getBillingAddress();
+
+        if ($shippingAddress) {
+            $shippingData = $this->dataObjectConverter->toFlatArray($shippingAddress, [], AddressInterface::class);
+            $shippingData['address_type'] = 'SHIPPING';
+            $addressData[] = array_merge($shippingData, $this->extractAddressData($shippingAddress));
+        }
+
+        if ($billingAddress) {
+            $billingData = $this->dataObjectConverter->toFlatArray($billingAddress, [], AddressInterface::class);
+            $billingData['address_type'] = 'BILLING';
+            $addressData[] = array_merge($billingData, $this->extractAddressData($billingAddress));
+        }
+
+        return $addressData;
+    }
+
+    /**
+     * Extract the necessary address fields from address model
+     *
+     * @param QuoteAddress $address
+     * @return array
+     */
+    private function extractAddressData(QuoteAddress $address): array
+    {
+        $addressData = [
+            'country' => [
+                'code' => $address->getCountryId(),
+                'label' => $address->getCountry()
+            ],
+            'region' => [
+                'code' => $address->getRegionCode(),
+                'label' => $address->getRegion()
+            ],
+            'street' => $address->getStreet(),
+            'selected_shipping_method' => [
+                'code' => $address->getShippingMethod(),
+                'label' => $address->getShippingDescription(),
+                'free_shipping' => $address->getFreeShipping(),
+            ],
+            'items_weight' => $address->getWeight(),
+            'customer_notes' => $address->getCustomerNotes()
+        ];
+
+        return $addressData;
+    }
+}
diff --git a/app/code/Magento/QuoteGraphQl/Model/Cart/SetShippingMethodOnCart.php b/app/code/Magento/QuoteGraphQl/Model/Cart/SetShippingMethodOnCart.php
new file mode 100644
index 000000000000..a630b2d07c7d
--- /dev/null
+++ b/app/code/Magento/QuoteGraphQl/Model/Cart/SetShippingMethodOnCart.php
@@ -0,0 +1,101 @@
+<?php
+/**
+ * Copyright © Magento, Inc. All rights reserved.
+ * See COPYING.txt for license details.
+ */
+declare(strict_types=1);
+
+namespace Magento\QuoteGraphQl\Model\Cart;
+
+use Magento\Framework\Exception\InputException;
+use Magento\Framework\Exception\NoSuchEntityException;
+use Magento\Framework\Exception\StateException;
+use Magento\Framework\GraphQl\Exception\GraphQlInputException;
+use Magento\Framework\GraphQl\Exception\GraphQlNoSuchEntityException;
+use Magento\Quote\Model\Quote;
+use Magento\Quote\Model\Quote\AddressFactory as QuoteAddressFactory;
+use Magento\Quote\Model\ResourceModel\Quote\Address as QuoteAddressResource;
+use Magento\Checkout\Model\ShippingInformationFactory;
+use Magento\Checkout\Api\ShippingInformationManagementInterface;
+use Magento\Checkout\Model\ShippingInformation;
+
+/**
+ * Class SetShippingMethodsOnCart
+ *
+ * Set shipping method for a specified shopping cart address
+ */
+class SetShippingMethodOnCart
+{
+    /**
+     * @var ShippingInformationFactory
+     */
+    private $shippingInformationFactory;
+
+    /**
+     * @var QuoteAddressFactory
+     */
+    private $quoteAddressFactory;
+
+    /**
+     * @var QuoteAddressResource
+     */
+    private $quoteAddressResource;
+
+    /**
+     * @var ShippingInformationManagementInterface
+     */
+    private $shippingInformationManagement;
+
+    /**
+     * @param ShippingInformationManagementInterface $shippingInformationManagement
+     * @param QuoteAddressFactory $quoteAddressFactory
+     * @param QuoteAddressResource $quoteAddressResource
+     * @param ShippingInformationFactory $shippingInformationFactory
+     */
+    public function __construct(
+        ShippingInformationManagementInterface $shippingInformationManagement,
+        QuoteAddressFactory $quoteAddressFactory,
+        QuoteAddressResource $quoteAddressResource,
+        ShippingInformationFactory $shippingInformationFactory
+    ) {
+        $this->shippingInformationManagement = $shippingInformationManagement;
+        $this->quoteAddressResource = $quoteAddressResource;
+        $this->quoteAddressFactory = $quoteAddressFactory;
+        $this->shippingInformationFactory = $shippingInformationFactory;
+    }
+
+    /**
+     * Sets shipping method for a specified shopping cart address
+     *
+     * @param Quote $cart
+     * @param int $cartAddressId
+     * @param string $carrierCode
+     * @param string $methodCode
+     * @throws GraphQlInputException
+     * @throws GraphQlNoSuchEntityException
+     */
+    public function execute(Quote $cart, int $cartAddressId, string $carrierCode, string $methodCode): void
+    {
+        $quoteAddress = $this->quoteAddressFactory->create();
+        $this->quoteAddressResource->load($quoteAddress, $cartAddressId);
+
+        /** @var ShippingInformation $shippingInformation */
+        $shippingInformation = $this->shippingInformationFactory->create();
+
+        /* If the address is not a shipping address (but billing) the system will find the proper shipping address for
+           the selected cart and set the information there (actual for single shipping address) */
+        $shippingInformation->setShippingAddress($quoteAddress);
+        $shippingInformation->setShippingCarrierCode($carrierCode);
+        $shippingInformation->setShippingMethodCode($methodCode);
+
+        try {
+            $this->shippingInformationManagement->saveAddressInformation($cart->getId(), $shippingInformation);
+        } catch (NoSuchEntityException $exception) {
+            throw new GraphQlNoSuchEntityException(__($exception->getMessage()));
+        } catch (StateException $exception) {
+            throw new GraphQlInputException(__($exception->getMessage()));
+        } catch (InputException $exception) {
+            throw new GraphQlInputException(__($exception->getMessage()));
+        }
+    }
+}
diff --git a/app/code/Magento/QuoteGraphQl/Model/Resolver/CartAddresses.php b/app/code/Magento/QuoteGraphQl/Model/Resolver/CartAddresses.php
new file mode 100644
index 000000000000..69544672bf12
--- /dev/null
+++ b/app/code/Magento/QuoteGraphQl/Model/Resolver/CartAddresses.php
@@ -0,0 +1,48 @@
+<?php
+/**
+ * Copyright © Magento, Inc. All rights reserved.
+ * See COPYING.txt for license details.
+ */
+declare(strict_types=1);
+
+namespace Magento\QuoteGraphQl\Model\Resolver;
+
+use Magento\Framework\Exception\LocalizedException;
+use Magento\Framework\GraphQl\Config\Element\Field;
+use Magento\Framework\GraphQl\Query\ResolverInterface;
+use Magento\Framework\GraphQl\Schema\Type\ResolveInfo;
+use Magento\QuoteGraphQl\Model\Cart\Address\AddressDataProvider;
+
+/**
+ * @inheritdoc
+ */
+class CartAddresses implements ResolverInterface
+{
+    /**
+     * @var AddressDataProvider
+     */
+    private $addressDataProvider;
+
+    /**
+     * @param AddressDataProvider $addressDataProvider
+     */
+    public function __construct(
+        AddressDataProvider $addressDataProvider
+    ) {
+        $this->addressDataProvider = $addressDataProvider;
+    }
+
+    /**
+     * @inheritdoc
+     */
+    public function resolve(Field $field, $context, ResolveInfo $info, array $value = null, array $args = null)
+    {
+        if (!isset($value['model'])) {
+            throw new LocalizedException(__('"model" value should be specified'));
+        }
+
+        $cart = $value['model'];
+
+        return $this->addressDataProvider->getCartAddresses($cart);
+    }
+}
diff --git a/app/code/Magento/QuoteGraphQl/Model/Resolver/SetShippingMethodsOnCart.php b/app/code/Magento/QuoteGraphQl/Model/Resolver/SetShippingMethodsOnCart.php
new file mode 100644
index 000000000000..920829f5d67b
--- /dev/null
+++ b/app/code/Magento/QuoteGraphQl/Model/Resolver/SetShippingMethodsOnCart.php
@@ -0,0 +1,99 @@
+<?php
+/**
+ * Copyright © Magento, Inc. All rights reserved.
+ * See COPYING.txt for license details.
+ */
+declare(strict_types=1);
+
+namespace Magento\QuoteGraphQl\Model\Resolver;
+
+use Magento\Framework\GraphQl\Exception\GraphQlInputException;
+use Magento\Framework\GraphQl\Query\ResolverInterface;
+use Magento\Framework\GraphQl\Config\Element\Field;
+use Magento\Framework\GraphQl\Schema\Type\ResolveInfo;
+use Magento\Framework\Stdlib\ArrayManager;
+use Magento\QuoteGraphQl\Model\Cart\GetCartForUser;
+use Magento\QuoteGraphQl\Model\Cart\SetShippingMethodOnCart;
+
+/**
+ * Class SetShippingMethodsOnCart
+ *
+ * Mutation resolver for setting shipping methods for shopping cart
+ */
+class SetShippingMethodsOnCart implements ResolverInterface
+{
+    /**
+     * @var SetShippingMethodOnCart
+     */
+    private $setShippingMethodOnCart;
+
+    /**
+     * @var ArrayManager
+     */
+    private $arrayManager;
+
+    /**
+     * @var GetCartForUser
+     */
+    private $getCartForUser;
+
+    /**
+     * @param ArrayManager $arrayManager
+     * @param GetCartForUser $getCartForUser
+     * @param SetShippingMethodOnCart $setShippingMethodOnCart
+     */
+    public function __construct(
+        ArrayManager $arrayManager,
+        GetCartForUser $getCartForUser,
+        SetShippingMethodOnCart $setShippingMethodOnCart
+    ) {
+        $this->arrayManager = $arrayManager;
+        $this->getCartForUser = $getCartForUser;
+        $this->setShippingMethodOnCart = $setShippingMethodOnCart;
+    }
+
+    /**
+     * @inheritdoc
+     */
+    public function resolve(Field $field, $context, ResolveInfo $info, array $value = null, array $args = null)
+    {
+        $shippingMethods = $this->arrayManager->get('input/shipping_methods', $args);
+        $maskedCartId = $this->arrayManager->get('input/cart_id', $args);
+
+        if (!$maskedCartId) {
+            throw new GraphQlInputException(__('Required parameter "cart_id" is missing'));
+        }
+        if (!$shippingMethods) {
+            throw new GraphQlInputException(__('Required parameter "shipping_methods" is missing'));
+        }
+
+        $shippingMethod = reset($shippingMethods); // This point can be extended for multishipping
+
+        if (!$shippingMethod['cart_address_id']) {
+            throw new GraphQlInputException(__('Required parameter "cart_address_id" is missing'));
+        }
+        if (!$shippingMethod['shipping_carrier_code']) {
+            throw new GraphQlInputException(__('Required parameter "shipping_carrier_code" is missing'));
+        }
+        if (!$shippingMethod['shipping_method_code']) {
+            throw new GraphQlInputException(__('Required parameter "shipping_method_code" is missing'));
+        }
+
+        $userId = $context->getUserId();
+        $cart = $this->getCartForUser->execute((string) $maskedCartId, $userId);
+
+        $this->setShippingMethodOnCart->execute(
+            $cart,
+            $shippingMethod['cart_address_id'],
+            $shippingMethod['shipping_carrier_code'],
+            $shippingMethod['shipping_method_code']
+        );
+
+        return [
+            'cart' => [
+                'cart_id' => $maskedCartId,
+                'model' => $cart
+            ]
+        ];
+    }
+}
diff --git a/app/code/Magento/QuoteGraphQl/composer.json b/app/code/Magento/QuoteGraphQl/composer.json
index c9900dd5f315..f0d2eea9bcaf 100644
--- a/app/code/Magento/QuoteGraphQl/composer.json
+++ b/app/code/Magento/QuoteGraphQl/composer.json
@@ -6,6 +6,7 @@
         "php": "~7.1.3||~7.2.0",
         "magento/framework": "*",
         "magento/module-quote": "*",
+        "magento/module-checkout": "*",
         "magento/module-catalog": "*",
         "magento/module-store": "*"
     },
diff --git a/app/code/Magento/QuoteGraphQl/etc/schema.graphqls b/app/code/Magento/QuoteGraphQl/etc/schema.graphqls
index f692aa57b218..a6c56318d7a9 100644
--- a/app/code/Magento/QuoteGraphQl/etc/schema.graphqls
+++ b/app/code/Magento/QuoteGraphQl/etc/schema.graphqls
@@ -1,13 +1,87 @@
 # Copyright © Magento, Inc. All rights reserved.
 # See COPYING.txt for license details.
 
+type Query {
+    getAvailableShippingMethodsOnCart(input: AvailableShippingMethodsOnCartInput): AvailableShippingMethodsOnCartOutput @doc(description:"Returns available shipping methods for cart by address/address_id")
+}
+
 type Mutation {
     createEmptyCart: String @resolver(class: "\\Magento\\QuoteGraphQl\\Model\\Resolver\\CreateEmptyCart") @doc(description:"Creates empty shopping cart for guest or logged in user")
     applyCouponToCart(input: ApplyCouponToCartInput): ApplyCouponToCartOutput @resolver(class: "\\Magento\\QuoteGraphQl\\Model\\Resolver\\ApplyCouponToCart")
     removeCouponFromCart(input: RemoveCouponFromCartInput): RemoveCouponFromCartOutput @resolver(class: "\\Magento\\QuoteGraphQl\\Model\\Resolver\\RemoveCouponFromCart")
+    setShippingAddressesOnCart(input: SetShippingAddressesOnCartInput): SetShippingAddressesOnCartOutput
+    setBillingAddressOnCart(input: SetBillingAddressOnCartInput): SetBillingAddressOnCartOutput
+    setShippingMethodsOnCart(input: SetShippingMethodsOnCartInput): SetShippingMethodsOnCartOutput @resolver(class: "\\Magento\\QuoteGraphQl\\Model\\Resolver\\SetShippingMethodsOnCart")
     addSimpleProductsToCart(input: AddSimpleProductsToCartInput): AddSimpleProductsToCartOutput @resolver(class: "Magento\\QuoteGraphQl\\Model\\Resolver\\AddSimpleProductsToCart")
 }
 
+input SetShippingAddressesOnCartInput {
+    cart_id: String!
+    customer_address_id: Int # Can be provided in one-page checkout and is required for multi-shipping checkout
+    address: CartAddressInput
+    cart_items: [CartItemQuantityInput!]
+}
+
+input CartItemQuantityInput {
+    cart_item_id: Int!
+    quantity: Float!
+}
+
+input SetBillingAddressOnCartInput {
+    cart_id: String!
+    customer_address_id: Int
+    address: CartAddressInput
+    # TODO: consider adding "Same as shipping" option
+}
+
+input CartAddressInput {
+    firstname: String!
+    lastname: String!
+    company: String
+    street: [String!]!
+    city: String!
+    region: String
+    postcode: String
+    country_code: String!
+    telephone: String!
+    save_in_address_book: Boolean!
+}
+
+input SetShippingMethodsOnCartInput {
+    cart_id: String!
+    shipping_methods: [ShippingMethodForAddressInput!]!
+}
+
+input ShippingMethodForAddressInput {
+    cart_address_id: Int!
+    shipping_carrier_code: String!
+    shipping_method_code: String!
+}
+
+type SetBillingAddressOnCartOutput {
+    cart: Cart!
+}
+
+type SetShippingAddressesOnCartOutput {
+    cart: Cart!
+}
+
+type SetShippingMethodsOnCartOutput {
+    cart: Cart!
+}
+
+# If no address is provided, the system get address assigned to a quote
+# If there's no address at all - the system returns all shipping methods
+input AvailableShippingMethodsOnCartInput {
+    cart_id: String!
+    customer_address_id: Int
+    address: CartAddressInput
+}
+
+type AvailableShippingMethodsOnCartOutput {
+    available_shipping_methods: [CheckoutShippingMethod]
+}
+
 input ApplyCouponToCartInput {
     cart_id: String!
     coupon_code: String!
@@ -18,12 +92,56 @@ type ApplyCouponToCartOutput {
 }
 
 type Cart {
+    cart_id: String
     items: [CartItemInterface]
     applied_coupon: AppliedCoupon
+    addresses: [CartAddress]! @resolver(class: "\\Magento\\QuoteGraphQl\\Model\\Resolver\\CartAddresses")
 }
 
 type CartAddress {
-    applied_coupon: AppliedCoupon
+    firstname: String
+    lastname: String
+    company: String
+    street: [String]
+    city: String
+    region: CartAddressRegion
+    postcode: String
+    country: CartAddressCountry
+    telephone: String
+    address_type: AdressTypeEnum
+    selected_shipping_method: CheckoutShippingMethod
+    available_shipping_methods: [CheckoutShippingMethod]
+    items_weight: Float
+    customer_notes: String
+    cart_items: [CartItemQuantity]
+}
+
+type CartItemQuantity {
+    cart_item_id: String!
+    quantity: Float!
+}
+
+type CartAddressRegion {
+    code: String
+    label: String
+}
+
+type CartAddressCountry {
+    code: String
+    label: String
+}
+
+type CheckoutShippingMethod {
+    code: String
+    label: String
+    free_shipping: Boolean!
+    error_message: String
+    # TODO: Add more complex structure for shipping rates
+}
+
+enum AdressTypeEnum {
+    SHIPPING
+    BILLING
 }
 
 type AppliedCoupon {