The Gantt control will let the users move tasks (and milestones) in time.
The task groups are displayed in an Auto mode by default - their start and end will be calculated from children. In the Auto task group mode it's not possible to move the groups using drag and drop.
Task moving is enabled by default. The handling type is set to Notify - this means the task will be moved on the client side immediately, then the server will be notified using an AJAX call. No server-side refresh is required.
Read more about drag and drop Gantt task moving.
Read more about drag and drop Gantt task resizing.
Read more about Gantt row moving.
Read more about drag and drop link creating.