JavaScript exception handling involves the use of try, catch, throw, and finally statements to manage errors in code execution. The try statement allows for testing a block of code for errors, the catch statement handles any errors that occur, and the finally statement ensures a block of code runs regardless of the outcome. The throw statement is used to create custom errors. An example demonstrates a deliberate error by misspelling "alert" as "allert," showing how catch can handle this error by displaying a message. Additionally, the Rollbar JavaScript SDK is introduced as a tool to streamline error resolution, offering real-time tracking, analysis, and management of errors to enhance confidence in code deployment. Rollbar automates error monitoring and triaging, simplifying the process of fixing JavaScript errors.