Xenia Canary
Xenia Canary is an experimental fork of Xenia, the open source Xbox 360 emulator, and is now where most Xenia development happens. It gets new features, fixes and compatibility improvements first, and many games run better in Canary than in the original Xenia.
New builds are published automatically after each change, often several times a week, so the downloads here are dated rather than versioned. Builds are available for Windows and, as an AppImage, for Linux. It needs 64-bit Windows 10 or later (or Linux), a processor that supports AVX, and a graphics card that supports Direct3D 12 or Vulkan.
Compatibility varies a lot from game to game. The project keeps a game compatibility list on GitHub, so check it before you start.