This National Guard video, though dated, makes some essential points about combat use of the shotgun and includes a bit of history.
The video is only a quick overview of the shotgun as a military weapon, and it does not go into the finer points. For one thing, it does not touch upon the very important question of reloading the shotgun. In all, though, it is a solid presentation of the how and why of the fighting shotgun.
The contact information at the end of the film is outdated, by the way, so don't try to call.