For large commercial airliners it's been Boeing and Airbus since Lockheed exited (and Boeing ate McDonnell Douglas). Boeing is a publicly-held American company; Airbus is a government-subsidized multinational whose holders are English, French, German and Spanish. This is part of the acrimony; Boeing points at Airbus and argues they shouldn't have to compete with a government entity while Airbus points at Boeing and remarks on how much graft and corruption drives the US military space (while ignoring that Boeing largely makes commercial aircraft).
Lately, Bombardier is making a run at it, but they haven't sold many. Bombardier is Canadian and Boeing thinks they're cheating the same as Airbus. Embraer, a Brazilian firm, has also stepped up into larger planes with the E2, which has 200-odd orders. They've made a name for themselves in the "bigger than a Gulfstream, smaller than a 737" space and the E2 is at the larger end of that.
Meanwhile, Mitsubishi is throwing their hat into the ring. They've got orders and have done for eight years but they ain't delivering, from what I understand. Then of course the Chinese and the Russians showed up.
But so far, it's Airbus and Boeing. There's 300 Irkuts, 200 COMACs, a couple hundred Embraers and maybe 250 Mitsubishis in the pipeline but Boeing has 3700 orders for the 737MAX alone, and Airbus has 5,000 A320s in the works.
You'll notice none of those are jumbos. There's 1500 747s plying the skies already and 213 A380s; the controversy that Boeing may well have tricked Airbus into building the A380 in the first place doesn't speak well for its future.
I knew some of the guys on the Sonic Cruiser project. When it was revealed that maybe they were part of an elaborate ruse, none of them were surprised. Were they? Weren't they?
I don't think airbus would have come up with the notion that future air travel would be more concentrated and that airports would be bigger without Boeing giving them a nudge, but I'm biased.
Also worthy of note:
You don't stand up an aircraft company the way you stand up a motorcycle company. I'm not bullish on Mitsubishi. Irkut is Yakovlev and COMAC is the same damn design bureau as all their jets but Mitsubishi hasn't made aircraft, to the best of my knowledge, since this guy.