1. A method comprising: receiving, by a notification module operable by a computing device, an instruction to generate a contextual notification; responsive to determining, at a first time and based on a context of the computing device at the first time, that the contextual notification is relevant to a user of the computing device at the first time, assigning, by the notification module and based at least in part on the context of the computing device at the first time and notification information associated with the contextual notification, the contextual notification to a first notification class from a plurality of notification classes, wherein the context of the computing device comprises at least one of 1) information associated with a current task being performed by the computing device, 2) information associated with a user of the computing device, or 3) information associated with at least one sensor of the computing device; outputting, for display and in a format that is determined based at least in part on the first notification class to which the contextual notification is assigned, a graphical indication of the contextual notification; responsive to determining, at a second time and based on a context of the computing device at the second time, that the contextual notification is not relevant to the user of the computing device at the second time, assigning, by the notification module and based at least in part on the context of the computing device at the second time and the notification information, the contextual notification to a second notification class from the plurality of notification classes; and responsive to assigning the contextual notification to the second notification class, updating the graphical indication of the contextual notification.