To report on all SMS activity recorded in CiviCRM, you can run the Activities report, available here: Reports > Contact Reports.
The SMS activity types are "Inbound SMS", "Mass SMS" and "SMS delivery".
You can then filter by SMS activity type and further by:
- message status (e.g. completed/scheduled)
- date and time
- which group or tag the recipient is in
- and characteristics of the recipients themselves, such as their name and location.
Finally, to update the results click "Preview Report" at the bottom of the Filters window.