So the latest news is another attempt to make Washington, D.C., into a state. Right now it has electoral votes (which it was granted by constitutional amendment in 1964), but only a non-voting delegate in the House and no senators. Supposedly it is unique this way among federal enclaves (I haven't checked other countries).
Why is it this way at all? Because in the early republic, the states were jealous of each other and nobody wanted control of the federal capital to be under the control of any state other than their own. So they put it in no state. The Constitution provided for, and acts of Congress established, a ten mile square zone along the Potomac River between Maryland and Virginia, taken from bits of both states, exact site chosen by George Washington, who besides being a resident of the general region and the President, was also a surveyor by profession. They called it the District of Columbia. And in that zone, on the Maryland side of the river, they erected a Capitol and a Presidential Mansion (later called the White House) and a few other buildings, and that was about it for a long time. It was a manifestation of the 18th century passion for conquering swamps, which also gave us Versailles and Saint Petersburg. None were healthy places to live, and in the sketchy town of Washington for many years pretty much the only permanent residents were service personnel (including slaves, because this was the South). Congressmen rented rooms in boarding houses during the short Congressional sessions, and then went home.
So little was made of the District that the part on the other side of the river, which the feds were making no use of at all, was retroceded to Virginia. Meanwhile Washington, over on the other side, slowly became a city, and eventually a majority Black one. Many more government buildings were built, quasi-governmental institutions like the Smithsonian were established, other institutions dependent on government like lobbyists and think tanks took root, and more people began living there permanently. It passed 100,000 in 1870 and 500,000 in 1940.
The big change came with the New Deal and WW2, with the growth of the federal government and the development of air conditioning (which was also transforming Florida at the same time). During the war a huge new five-sided building was constructed to put the entire military bureaucracy under one roof, and due to lack of room in D.C. it was placed on the Virginia side of the river, in the retroceded section. Nowadays the metonym for the federal government and its appurtenances is "inside the Beltway," the Beltway being a highway loop that goes far outside the D.C. limits, encompassing establishments like the NIH in suburban Maryland, the Pentagon in retroceded Virginia, and the CIA in Virginia outside the retrocession.
So it no longer really matters what state the government is in - that state isn't going to control the government - and the idea of a federal enclave is obsolete; the central government is half outside it anyway. They could just retocede the rest to Maryland and have done with it, but that isn't considered practical. Instead, the idea of making it a state of its own, often thought of before, has been resurrected. Republicans are opposed, supposedly for constitutional reasons, but since those are easily brushed aside, it's because they don't want a state full of Democratic-voting Blacks. (D.C.'s electoral votes have gone to every Democratic candidate since they were granted, even McGovern and Dukakis.) Ironically, D.C. is getting less Black all the time. The city is rapidly gentrifying, and Blacks are moving out to the suburbs, especially Prince Georges County, Maryland, which is now far more Black than D.C. is. The city is now just under half Black; it used to be 70%.
One problem is the name. "District of Columbia" isn't suitable for a state, it honors Columbus whom we're not celebrating any more, and nobody calls it that anyway, it's "D.C." or "Washington, D.C." Some of the proposers are suggesting "Douglass Commonwealth," which sounds cool: it honors Frederick Douglass, much more honorable, and several existing states are already officially called Commonwealths, including Virginia. Another suggestion is "New Columbia" which is much less good; it preserves Columbus and doesn't preserve D.C., instead changing to N.C. which is already taken.
What interests me, as a geographic trivia nerd, is what happens to the federal enclave? The proposal is to limit it to a few central government buildings, but exactly what will be the extent? This article from a D.C. real estate site has one; here's a slightly revised version that annexes the Trump Hotel. Here's an earlier proposal encompassing much more area. And a much earlier one, from 1970, very close to the current plan.
The one genuine constitutional problem is that the reduced federal enclave of virtually nil resident population,* will, by virtue of the 23rd Amendment, still have 3 electoral votes, but the sponsors say it can be repealed.
I would ask, though, why do we need a federal enclave at all? Unless I missed something, the only constitutional provision regarding the location of the seat of government is in Article 1, Section 8, giving Congress jurisdiction "over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States." It permits one, but it doesn't read to me as if it requires it. And I don't think we need one any more, unless it were to include the entire Beltway, which is exactly what we're trying to avoid.
*Some comments say this includes the president and family. Not legally. All presidents have kept their voting addresses at their personal homes elsewhere, though DT tried to list the White House as his residence when he re-registered himself in Florida; Florida sent it back saying, "You idiot, you need a Florida residence to vote in Florida," so DT returned it listing Mar-a-Lago, which is what he'd been thinking of when he chose Florida in the first place.