diff --git a/sopel/irc/abstract_backends.py b/sopel/irc/abstract_backends.py
index e8b8ba914..080e9325d 100644
--- a/sopel/irc/abstract_backends.py
+++ b/sopel/irc/abstract_backends.py
@@ -15,6 +15,7 @@
 from __future__ import annotations
 
 import abc
+import logging
 from typing import Optional, TYPE_CHECKING
 
 from .utils import safe
@@ -41,6 +42,17 @@ def __init__(self, bot: AbstractBot):
     def is_connected(self) -> bool:
         """Tell if the backend is connected or not."""
 
+    def log_exception(self) -> None:
+        """Log an exception to ``sopel.exceptions``.
+
+        The IRC backend must use this method to log any exception that isn't
+        caught by the bot itself (i.e. while handling messages), such as
+        connection errors, SSL errors, etc.
+        """
+        err_log = logging.getLogger('sopel.exceptions')
+        err_log.exception('Exception in core')
+        err_log.error('----------------------------------------')
+
     @abc.abstractmethod
     def on_irc_error(self, pretrigger: PreTrigger) -> None:
         """Action to perform when the server sends an error event.
diff --git a/sopel/irc/backends.py b/sopel/irc/backends.py
index 0ccf5f286..9b42c3999 100644
--- a/sopel/irc/backends.py
+++ b/sopel/irc/backends.py
@@ -17,6 +17,7 @@
 import asyncio
 import logging
 import signal
+import socket
 import ssl
 import threading
 from typing import Dict, List, Optional, Tuple, TYPE_CHECKING
@@ -379,6 +380,7 @@ def get_connection_kwargs(self) -> Dict:
 
     async def _run_forever(self) -> None:
         self._loop = asyncio.get_running_loop()
+        connection_kwargs = self.get_connection_kwargs()
 
         # register signal handlers
         for quit_signal in QUIT_SIGNALS:
@@ -389,16 +391,78 @@ async def _run_forever(self) -> None:
         # open connection
         try:
             self._reader, self._writer = await asyncio.open_connection(
-                **self.get_connection_kwargs(),
+                **connection_kwargs,
             )
-        except ssl.SSLError:
-            LOGGER.exception('Unable to connect due to SSL error.')
+
+        # SSL Error
+        except ssl.SSLCertVerificationError as err:
+            LOGGER.error(
+                'Unable to connect due to an SSL validation error: %s',
+                err,
+            )
+            self.log_exception()
+            # tell the bot to quit without restart
+            self.bot.hasquit = True
+            self.bot.wantsrestart = False
+            return
+        except ssl.SSLError as err:
+            LOGGER.error('Unable to connect due to an SSL error: %s', err)
+            self.log_exception()
+            # tell the bot to quit without restart
+            self.bot.hasquit = True
+            self.bot.wantsrestart = False
+            return
+
+        # Specific connection error
+        except socket.gaierror as err:
+            LOGGER.error(
+                'Unable to connect due to invalid IRC server address: %s',
+                err,
+            )
+            LOGGER.warning(
+                'You should verify that "%s:%s" is the correct address '
+                'to connect to the IRC server.',
+                connection_kwargs.get('host'),
+                connection_kwargs.get('port'),
+            )
+            self.log_exception()
             # tell the bot to quit without restart
             self.bot.hasquit = True
             self.bot.wantsrestart = False
             return
-        except Exception:
-            LOGGER.exception('Unable to connect.')
+        except TimeoutError as err:
+            LOGGER.error('Unable to connect due to a timeout: %s', err)
+            self.log_exception()
+            # tell the bot to quit without restart
+            self.bot.hasquit = True
+            self.bot.wantsrestart = False
+            return
+
+        # Generic connection error (OSError is used for any connection error)
+        except OSError as err:
+            LOGGER.error(
+                'Unable to connect: %s',
+                err,
+            )
+            LOGGER.warning(
+                'You should verify that "%s:%s" is the correct address '
+                'to connect to the IRC server.',
+                connection_kwargs.get('host'),
+                connection_kwargs.get('port'),
+            )
+            self.log_exception()
+            # tell the bot to quit without restart
+            self.bot.hasquit = True
+            self.bot.wantsrestart = False
+            return
+
+        # Unexpected error
+        except Exception as err:
+            LOGGER.error(
+                'Unable to connect due to an unexpected error: %s',
+                err,
+            )
+            self.log_exception()
             # until there is a way to prevent an infinite loop of connection
             # error and reconnect, we have to tell the bot to quit here
             # TODO: prevent infinite connection failure loop