diff --git a/boa/src/syntax/parser/expression/assignment/conditional.rs b/boa/src/syntax/parser/expression/assignment/conditional.rs
new file mode 100644
index 00000000000..874aa950c9d
--- /dev/null
+++ b/boa/src/syntax/parser/expression/assignment/conditional.rs
@@ -0,0 +1,79 @@
+//! Conditional operator parsing.
+//!
+//! More information:
+//!  - [MDN documentation][mdn]
+//!  - [ECMAScript specification][spec]
+//!
+//! [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Conditional_Operator
+//! [spec]: https://tc39.es/ecma262/#sec-conditional-operator
+
+use crate::syntax::{
+    ast::{node::Node, punc::Punctuator, token::TokenKind},
+    parser::{
+        expression::{AssignmentExpression, LogicalORExpression},
+        AllowAwait, AllowIn, AllowYield, Cursor, ParseResult, TokenParser,
+    },
+};
+
+/// Conditional expression parsing.
+///
+/// More information:
+///  - [MDN documentation][mdn]
+///  - [ECMAScript specification][spec]
+///
+/// [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Conditional_Operator
+/// [spec]: https://tc39.es/ecma262/#prod-ConditionalExpression
+#[derive(Debug, Clone, Copy)]
+pub(in crate::syntax::parser::expression) struct ConditionalExpression {
+    allow_in: AllowIn,
+    allow_yield: AllowYield,
+    allow_await: AllowAwait,
+}
+
+impl ConditionalExpression {
+    /// Creates a new `ConditionalExpression` parser.
+    pub(in crate::syntax::parser::expression) fn new<I, Y, A>(
+        allow_in: I,
+        allow_yield: Y,
+        allow_await: A,
+    ) -> Self
+    where
+        I: Into<AllowIn>,
+        Y: Into<AllowYield>,
+        A: Into<AllowAwait>,
+    {
+        Self {
+            allow_in: allow_in.into(),
+            allow_yield: allow_yield.into(),
+            allow_await: allow_await.into(),
+        }
+    }
+}
+
+impl TokenParser for ConditionalExpression {
+    type Output = Node;
+
+    fn parse(self, cursor: &mut Cursor<'_>) -> ParseResult {
+        // TODO: coalesce expression
+        let lhs = LogicalORExpression::new(self.allow_in, self.allow_yield, self.allow_await)
+            .parse(cursor)?;
+
+        if let Some(tok) = cursor.next() {
+            if tok.kind == TokenKind::Punctuator(Punctuator::Question) {
+                let then_clause =
+                    AssignmentExpression::new(self.allow_in, self.allow_yield, self.allow_await)
+                        .parse(cursor)?;
+                cursor.expect(Punctuator::Colon, "conditional expression")?;
+
+                let else_clause =
+                    AssignmentExpression::new(self.allow_in, self.allow_yield, self.allow_await)
+                        .parse(cursor)?;
+                return Ok(Node::conditional_op(lhs, then_clause, else_clause));
+            } else {
+                cursor.back();
+            }
+        }
+
+        Ok(lhs)
+    }
+}
diff --git a/boa/src/syntax/parser/expression/assignment/exponentiation.rs b/boa/src/syntax/parser/expression/assignment/exponentiation.rs
new file mode 100644
index 00000000000..5da2b310326
--- /dev/null
+++ b/boa/src/syntax/parser/expression/assignment/exponentiation.rs
@@ -0,0 +1,94 @@
+//! Exponentiation operator parsing.
+//!
+//! More information:
+//!  - [MDN documentation][mdn]
+//!  - [ECMAScript specification][spec]
+//!
+//! [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Arithmetic_Operators#Exponentiation
+//! [spec]: https://tc39.es/ecma262/#sec-exp-operator
+
+use crate::syntax::{
+    ast::{
+        keyword::Keyword,
+        node::Node,
+        op::{BinOp, NumOp},
+        punc::Punctuator,
+        token::TokenKind,
+    },
+    parser::{
+        expression::{unary::UnaryExpression, update::UpdateExpression},
+        AllowAwait, AllowYield, Cursor, ParseResult, TokenParser,
+    },
+};
+
+/// Parses an exponentiation expression.
+///
+/// More information:
+///  - [MDN documentation][mdn]
+///  - [ECMAScript specification][spec]
+///
+/// [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Arithmetic_Operators#Exponentiation
+/// [spec]: https://tc39.es/ecma262/#prod-ExponentiationExpression
+#[derive(Debug, Clone, Copy)]
+pub(in crate::syntax::parser::expression) struct ExponentiationExpression {
+    allow_yield: AllowYield,
+    allow_await: AllowAwait,
+}
+
+impl ExponentiationExpression {
+    /// Creates a new `ExponentiationExpression` parser.
+    pub(in crate::syntax::parser::expression) fn new<Y, A>(allow_yield: Y, allow_await: A) -> Self
+    where
+        Y: Into<AllowYield>,
+        A: Into<AllowAwait>,
+    {
+        Self {
+            allow_yield: allow_yield.into(),
+            allow_await: allow_await.into(),
+        }
+    }
+}
+
+impl ExponentiationExpression {
+    /// Checks by looking at the next token to see whether it's a unary operator or not.
+    fn is_unary_expression(cursor: &mut Cursor<'_>) -> bool {
+        if let Some(tok) = cursor.peek(0) {
+            match tok.kind {
+                TokenKind::Keyword(Keyword::Delete)
+                | TokenKind::Keyword(Keyword::Void)
+                | TokenKind::Keyword(Keyword::TypeOf)
+                | TokenKind::Punctuator(Punctuator::Add)
+                | TokenKind::Punctuator(Punctuator::Sub)
+                | TokenKind::Punctuator(Punctuator::Not)
+                | TokenKind::Punctuator(Punctuator::Neg) => true,
+                _ => false,
+            }
+        } else {
+            false
+        }
+    }
+}
+
+impl TokenParser for ExponentiationExpression {
+    type Output = Node;
+
+    fn parse(self, cursor: &mut Cursor<'_>) -> ParseResult {
+        if Self::is_unary_expression(cursor) {
+            return UnaryExpression::new(self.allow_yield, self.allow_await).parse(cursor);
+        }
+
+        let lhs = UpdateExpression::new(self.allow_yield, self.allow_await).parse(cursor)?;
+        if let Some(tok) = cursor.next() {
+            if let TokenKind::Punctuator(Punctuator::Exp) = tok.kind {
+                return Ok(Node::bin_op(
+                    BinOp::Num(NumOp::Exp),
+                    lhs,
+                    self.parse(cursor)?,
+                ));
+            } else {
+                cursor.back();
+            }
+        }
+        Ok(lhs)
+    }
+}
diff --git a/boa/src/syntax/parser/expression/unary.rs b/boa/src/syntax/parser/expression/unary.rs
new file mode 100644
index 00000000000..14a2c7a29be
--- /dev/null
+++ b/boa/src/syntax/parser/expression/unary.rs
@@ -0,0 +1,79 @@
+//! Unary operator parsing.
+//!
+//! More information:
+//!  - [MDN documentation][mdn]
+//!  - [ECMAScript specification][spec]
+//!
+//! [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Expressions_and_Operators#Unary
+//! [spec]: https://tc39.es/ecma262/#sec-unary-operators
+
+use crate::syntax::{
+    ast::{keyword::Keyword, node::Node, op::UnaryOp, punc::Punctuator, token::TokenKind},
+    parser::{
+        expression::update::UpdateExpression, AllowAwait, AllowYield, Cursor, ParseError,
+        ParseResult, TokenParser,
+    },
+};
+
+/// Parses a unary expression.
+///
+/// More information:
+///  - [MDN documentation][mdn]
+///  - [ECMAScript specification][spec]
+///
+/// [mdn]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Expressions_and_Operators#Unary
+/// [spec]: https://tc39.es/ecma262/#prod-UnaryExpression
+#[derive(Debug, Clone, Copy)]
+pub(super) struct UnaryExpression {
+    allow_yield: AllowYield,
+    allow_await: AllowAwait,
+}
+
+impl UnaryExpression {
+    /// Creates a new `UnaryExpression` parser.
+    pub(super) fn new<Y, A>(allow_yield: Y, allow_await: A) -> Self
+    where
+        Y: Into<AllowYield>,
+        A: Into<AllowAwait>,
+    {
+        Self {
+            allow_yield: allow_yield.into(),
+            allow_await: allow_await.into(),
+        }
+    }
+}
+
+impl TokenParser for UnaryExpression {
+    type Output = Node;
+
+    fn parse(self, cursor: &mut Cursor<'_>) -> ParseResult {
+        let tok = cursor.next().ok_or(ParseError::AbruptEnd)?;
+        match tok.kind {
+            TokenKind::Keyword(Keyword::Delete) => {
+                Ok(Node::unary_op(UnaryOp::Delete, self.parse(cursor)?))
+            }
+            TokenKind::Keyword(Keyword::Void) => {
+                Ok(Node::unary_op(UnaryOp::Void, self.parse(cursor)?))
+            }
+            TokenKind::Keyword(Keyword::TypeOf) => {
+                Ok(Node::unary_op(UnaryOp::TypeOf, self.parse(cursor)?))
+            }
+            TokenKind::Punctuator(Punctuator::Add) => {
+                Ok(Node::unary_op(UnaryOp::Plus, self.parse(cursor)?))
+            }
+            TokenKind::Punctuator(Punctuator::Sub) => {
+                Ok(Node::unary_op(UnaryOp::Minus, self.parse(cursor)?))
+            }
+            TokenKind::Punctuator(Punctuator::Neg) => {
+                Ok(Node::unary_op(UnaryOp::Tilde, self.parse(cursor)?))
+            }
+            TokenKind::Punctuator(Punctuator::Not) => {
+                Ok(Node::unary_op(UnaryOp::Not, self.parse(cursor)?))
+            }
+            _ => {
+                cursor.back();
+                UpdateExpression::new(self.allow_yield, self.allow_await).parse(cursor)
+            }
+        }
+    }
+}