Why are the princes and princesses of Greece titled as Prince or Princess of Greece and Denmark?

I have recently taken an interest in several of the royal families, and when researching The Royal Family of Denmark, I found that their Greek relatives are titled as Princes of Greece and Denmark and wondered how this came to be? I know that Queen Anne Marie was born a Princess of Denmark, but I didn't know that the Danish monarchy ped titles down through the female line... Why do the Greeks possess the two titles?