Mule ESB provides options for handling errors through exception strategies. The default exception strategy implicitly handles all messaging exceptions by rolling back transactions and logging exceptions. Alternative exception strategies include catch, which commits transactions and consumes messages; rollback, which attempts to redeliver messages before committing failed transactions; reference, which refers to a global exception strategy; and choice, which customizes error handling based on message content. Exception strategies provide flexible ways to manage errors within Mule applications and flows.