This area of spectacular scenery is where US astronauts train before a mission.
The lunar landscapes are breathtaking and the area is desert-like. You can only get there in the summer because the roads to inland Iceland are closed throughout the rest of the year when the weather conditions are too dangerous for crossing the ford which leads to the campsite. While hiking, you'll come across many sulphur fumaroles, black lava flows and impressive rocks, as well as patches of snow, even in the summer.
Before returning to the campsite, go swimming in a 40-degree hot water spring surrounded by mountains. It's a real moment of happiness. Getting out and into the cold is not quite as pleasant though, so make sure you remember your towels and fleeces and get dressed quickly!
The trek up Thorsmörk was highly recommended to me. It takes three days to complete and I've included it as part of my itinerary for my next trip to Iceland.