The API itself supports some very cool compute functionality, such as asynchronously scheduled compute jobs. However, this functionality only exists on AMD hardware (to my knowledge). NVIDIA doesn't support it in HW (yet), and I don't _think_ it's in Intel HW natively. I don't think I've seen it in any other compute API either.

I've seen asynchronous DMAs + command execution (copy engine) exposed in some APIs, but not asynchronous compute shaders.