An idea that was stalled in Congress a couple of years ago, is now being reconsidered. The Senate Homeland Security & Governmental Affairs Committee has approved a bill to allow the District of Columbia to elect a voting member of the U.S. House of Representatives. Here are accounts of that action from the committee, and from The New York Times.
The proposal is in the same form as similar legislation in the previous Congress. It would expand the House by two seats, to 437. The other of those two new seats would go to the state that was closest to qualifying for an additional seat, in the apportionment after the 2000 census.
That math results in a politically convenient balance. The other seat would go to Utah, one of the most heavily Republican states. So, the Democrats' numerical lead over the Republicans in the House would remain unchanged.
However, as noted in the Times piece, Republicans are concerned about creating a precedent that would eventually result in creating two Senate seats for the District. Assuming that no one is willing to allow Utah four senators, there seems to be no way to strike a balance similar to that which is proposed for the House.
I think this proposal can be faulted on procedural grounds, but not in terms of equity. It's always been a strange anomaly that those who live among the central institutions of American democracy have limited political rights. Washingtonians were given a place in the electoral college, effective with the 1964 election. They subsequently gained the right to elect their municipal government. It's difficult to argue, except on nakedly partisan grounds, that they should be deprived of full congressional representation.
D.C. drivers display a hallowed American slogan on their license plates: "Taxation Without Representation".
The procedural question, of course, is whether this should instead be accomplished by constitutional amendment. The District's right to vote for president and vice president was implemented that way.
That would require supermajorities in both houses of Congress, as well as ratification by 38 state legislatures. A bit more difficult than a simple majority in the House, potentially a 60-vote supermajority in the Senate, and the signature of a president who is already on record supporting the plan.
A while back, the Congress tried to statutorily implement the line-item veto for appropriation bills, which was ruled unconstitutional by the Supreme Court. I would expect quite a few sparks to fly, if the D.C. representation issue faces a similar fate.
UPDATE: In response to the comment regarding the notion of returning the District to Maryland, Wikipedia has an article on that. Two problems are cited: 1) Maryland is apparently unwilling to take it back, and 2) it would be more complicated than the retrocession of the Virginia portion, because the main federal government institutions were always on the Maryland side.