Besides the email notifications which you can set in the Project settings area of a project, you will also receive in app notifications in the top left corner.
This saves time because you don't have to go to your inbox in order to see updates about tasks, projects, files etc.
Here are the types of notifications that will be displayed in this area:
Task budget threshold reached
Task status changed
Task priority changed
New booking created for you
Project file uploaded
Task file uploaded
Discussion file uploaded
Mentioned in task
Mentioned in discussion
Invoice created based on recurring profile
If you wish to mark them as read, hover over the desired notification and click on the Mark as read checkbox on the right or Mark all as read on the top.