Within Teamwork, you can view and filter your unread comments via the My Work area.
Select My Work from the main navigation menu on the left of your site. Click the More tab in the horizontal navigation menu and choose Unread Comments from the dropdown.

Click the filters button in the top right to open the filters pane.

Project
Choose which project(s) you want to include related unread comments from.

Comment Type
You can select which comment types to include, such as task and milestone comments. You can also select all comments to include everything.

Date
Select a date range for your unread comments, such as anytime, today, this week, or last month.

Author
Choose to filter to comments written by certain users.

Options
Filter to only unread comments within your starred projects.

Reordering filters
You can customize the order of the filters in the filters pane by dragging and dropping them to another position.

Saving filters
Once you have applied your filter preferences, you can choose to save the filter to use again. Select the Save Filter option at the bottom of the filters pane.
You can then select to apply one of your saved filters from the Saved Filters tab of the filters pane.

When a filter is applied, you will see it noted at the top of the page. You can also change quickly between your saving filters by clicking the currently active filter's name and choosing another from the dropdown.

Note: Saved filters are available on paid Teamwork subscriptions.
For more information, see: Viewing Your Unread Comments