To report on all SMS messages sent in CiviCRM, you can run an activity report, available here: Reports > Activity Report.
First, you will need to filter the activity type to either "BULK SMS" or "Text Message (SMS)"; select "BULK SMS if you sent the message to a mailing list, and "Text Message (SMS)" if you created it within a contact or advanced search (you may also select both by holding CTRL or CMD while you click). You can then filter further by:
All of these settings can be found by clicking the "Report Criteria" banner at the top of the report page.
Finally, to update the results click "Preview Report" at the bottom of the criteria section.