Is it illegal to have a katana?

Is it truly illegal to possess a katana in my possession? I've heard conflicting opinions on the matter and am seeking clarification. Do the laws surrounding the ownership of swords vary from state to state, or is there a universal regulation in place? Are there any specific conditions under which owning a katana would be deemed legal, such as having a permit or certification? Furthermore, if I were to purchase a katana for collection or display purposes, would I be breaking any laws by doing so? I would greatly appreciate your insight on this matter.