Within Teamwork, you can enable desktop alerts on your profile so you can see notifications from your site without having to keep checking your email.
You will see alerts for updates where you have been notified whenever you do not have the tab for Teamwork in focus in your browser, so you just need to keep it open in the background.
To enable, click your profile avatar in the bottom left of your site and select Edit my details from the pop-out menu.
In the user details modal, go to the Preferences tab where you can toggle on the Enable desktop alerts for important notifications option.
If you enable this setting, when you are notified of activity on a project (for example, if someone adds a comment or assigns a task to you and chooses to notify you) this will now show in the lower right of your screen.
Note: You may be prompted in your browser to allow the alerts and you will need to grant permission before alerts will show.
For more information, see: Filtering the Updates Showing Under the Notification Bell