I'm interested to see Captain America: Civil War, but I haven't been keeping up with the Marvel Cinematic Universe very well. I've seen the first Iron Man, Thor, and Captain America films, half of the first Avengers when it was running on television, and Guardians of the Galaxy. 

From what I've read, I gather that Age of Ultron and The Winter Soldier are pretty important background for Civil War. What about the others—Iron Man 2 and 3, Ant Man, Thor 2? Will I understand Civil War if I haven't seen them?