Are katanas legal in America?

I'm curious to know, are katanas, the traditional Japanese swords, considered legal to own and possess in the United States? Are there any restrictions or regulations that govern their ownership? If so, what are the specific guidelines one needs to follow to ensure they're in compliance with the law? Additionally, how does the legality of katanas vary from state to state? It would be interesting to understand the legal landscape surrounding these unique and historic weapons.