You've probably heard of or seen some of the weird stuff this two-man band does; odd face makeup, strange wardrobe, a few fast-paced electronic songs. It takes some getting used to, but Twenty One Pilots' music is some powerful and interesting stuff. It's hard to describe as one genre - sort of alternative/indie/electronic with some weird kind of rap, and each song is really different. Their lyrics, though, that's what gets you - there are some powerful things present in lead singer/songwriter Tyler Joseph's words. He talks about depression, anxiety, and other issues he and lots of people have to deal with. A lot of it is really relatable and eye-opening, but also sad. They can really help you through some tough times, though.
I'd recommend Polarize and Hometown if you're giving them a listen for the first time.
P.S. - My favourites are Trees and A Car, A Torch, A Death if you want to take a listen to those too. Or just listen to them all. That's good too.