The very general idea behind the lack of political representation for DC is that since it is the site of the federal government, it shouldn't be located in an actual state. Being located in a state would make it dependent upon that state's state government and the Founders wanted the federal government to be totally independent of all the states. Since DC isn't a state, they can't have members in Congress, or so some people claim, and so it works out in reality so far.

As for Puerto Rico, it is kind of the same thing. It is a US protectorate, but it isn't officially a state, so they can't have real representatives in Congress. There is a loud and ongoing debate on whether the people of Puerto Rico want to become a state, whether the US wants to accept them as a state, and whether it would be a good thing for them in terms of economy, government, ect, but so far they haven't signed on the dotted line.