The Russian Club Championship started on Sunday, May 1 and continues through May 10. Among the heavy hitters who have played so far there's Sergey Karjakin, Alexander Grischuk, Peter Svidler - to include only the players over 2750 - and Vladimir Kramnik is supposed to jump in at some point as well.
On Wednesday, Ding Liren and Wesley So will begin a four-game match in China. (Or maybe there will be four classical games and some additional rapid and/or blitz games. All I know thus far is the very little given in the "Future Events" section of this page. Further details would be appreciated.)