Royalty generally married into other royal lines, and with marriage came inheritances of both lands and titles from both sides of royal lineages, so that the King of England (for instance) can also be the Duke of Normandy. The family tree on this site gives a breakdown of the familial relations between the three dynasties.

There's a really good book called George, Nicholas, and Wilhelm: Three Cousins that talks about their relationships, the politics of the time, and how WWI happened between their countries.