When someone gives you a compliment, what is the proper response?

Compliments flatter me deeply, but they also make me feel really awkward because other than saying “thank you”, at the very least, I honestly am not sure where to go from there.

I usually feel compelled to compliment the person back, but shouldn’t I just be able to accept the compliment? Responding to a compliment with a compliment doesn’t feel right sometimes, though. I’ve trained myself to say “thank you” instead of directly deflecting, maybe I am deflecting their compliment in a different way. But people generally like being complimented, no? I’m not sure what I’m supposed to do or what other people do.

What is the right way to handle a compliment?