Assigning a task to a user is really important in teams. It will notify the user and helps you to set responsibility for a task.
The user avatar is displayed at the top right of each assigned task.
You can assign a task from both the project board and the task dialog.
Assigning from the project board
Simply hover over the right top corner of an unassigned task and click on the question mark to open the member list. Click on the avatar or name of a user to assign the task.
Assigning from the task dialog
The current assigned person is always shown at the top of the task dialog. Click on "Not Assigned" to open the member list. You can click on the avatar or name of a user here as well to assign the task.
You can easily show all tasks of one assignee by clicking on an avatar in the right members bar.