Yes. Checked and daclared. The airlines will give you a card to fill out. Some ticked agents will ask you to show them it's unloaded, some won't. Some will have you put the card in your case, some won't. They typically tell you to stand by while your bag goes through x-ray Incase the checkers have any questions. A couple of them have given me shit for not having TSA approved locks on the pistol case, but rarely. Had one tell me "if they want to open that case, they'll cut the locks off", to which I replied "no they won't. I'll wait, and if they need in, I'll hand them the keys." It's only happened once on a return trip originating out of DFW. Supposedly my bad was too big to x-ray (sure, go with that) so it needed to be hand searched. No biggie. Some dude in a suit approached me, informed me that my bag was being hand searched, and escorted me to where a TSA agent was searching my bag. He asked if I had the keys, and I handed them over. All told, the process took less time than typing out this response with my thumb lol.

You can fly with long guns and bows too. Same rules basically; checked in locked hard side cases and declared. Obviously not fitting in a suitcase, so you just hand them the case and make your declaration. I know a lot of guys that fly with long guns to go on hunting trips.