The first, which is not so interesting this year because so many of the best players aren't participating, is the World Junior Championship. The top seed, Jan-Krzysztof Duda of Poland, is the 7th ranked junior in the world and is currently tied for first with Jorden van Foreest of the Netherlands; both players have 5/6. There are two other 2600s in the event (Jorge Cori of Peru and Karen Gregoryan of Armenia), but there's no Wei Yi, Vladislav Artemiev, Daniil Dubov, Ivan Bukavshin or ex-2700 player Richard Rapport. The top American juniors Daniel Naroditsky, John Burke and Sam Sevian aren't playing either, and I have no idea why not (except in Sevian's case; he's playing in the World Cup). So it's a disappointing turnout from my point of view, but if your favorite "horse" is running by all means enjoy the show! It's a 13-round event, so there's still a long way to go.
The other world championship isn't labeled as such, but unlike this farce it's the real deal; all the engines are playing with the same hardware. The 8th season of the Thoresen Chess Engines Competition (TCEC) is underway, and the stage 1b qualifier is getting close to the end. Defending champion Komodo (now up to version 9.1) won the 1a qualifier with 9/11, surprisingly just half a point ahead of Gull (version 3), while last year's runner-up Stockfish (300815, e.g. a build released August 30 of this year) is mashing the field in the 1b qualifier with 8/8 so far, including a win over Houdini (still version 4).