Bulgaria has been under a variety of rulers over its history. Most well known is when it was part of the Communist Soviet bloc. Just walking through Sofia you can see the remnants of this period of their history by the number of Communist-era buildings.
When I was researching before the trip, I came across a suggestion to visit The Red Flat. This is a small museum showing a regular Bulgarian family's apartment. With your ticket (which you purchase in a really cool gift shop filled with items from local artists), you have basically unlimited time to spend in the apartment and a very thorough audio guide telling you about all aspects of the items in the home, life in Communist Bulgaria and more. It was so fascinating!
Another part of the trip that was really fascinating was the Museum of Socialist Art. After Communism fell, they took a lot of the statues erected during that time and placed them outside this museum. It is a great way to connect with history. The grounds were filled with both well-known people (like Lenin) and statues of everyday workers. There were also many statues of women which I was surprised by.
The inside of the museum had some artwork that was not as interesting, but the ticket is very affordable so why not check it out?