This is an excellent video which describes the use of the shotgun in a portion of American SF during the GWOT era:
Mostly what you would expect, guns used as breaching tools. But they were also used as primary weapons in expected close quarters situations.
The repeating shotgun has been involved in most of the fights the US has been involved with since its invention. It was used effectively in the Philippine campaign as it turned out to have actual stopping power. It was used to a limited extent in WWI where the paper ammunition was a problem, ultimately breeding all brass shells. Of course it saw use in WWII and Vietnam as well.
Most don't know that the shotgun was even active with Taskforce Ranger. When I did 1301 armorer training the instructor was in Taskforce Ranger and related that Somalis would swarm vehicles and shotguns loaded with buckshot proved effective at peeling them off without harming personnel inside the vehicles.
But it's neat to see some firsthand information about GWOT era use and combat with the shotgun. Note that Jeff discusses the effective dose of the 12 gauge vs. 5.56 multiple times.