Within Teamwork Projects, 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 you have been notified on whenever you don't have the tab in your browser for Teamwork Projects in focus so you just need to keep it open in the background.
To enable, click your profile image in the top right of your screen and choose Edit My Details from the drop-down menu.
In the edit details modal, select the Preferences tab. You can then toggle Enable desktop alerts for important notifications on.
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'll need to accept that before they will show.
For more information, see: Filtering the updates showing under the notification bell