After abandoning the Mantle API for DirectX 12, the situation ought to meanwhile be clear. There are, however, still a few other graphics APIs that aren't DirectX, thus AMD and the Khronos Group launched the Vulkan API. The final specifications of version 1.0 have been ratified, a first beta driver has been released.
The approach of the Vulkan API is similar to Mantle. The point is to gain a deeper control of the hardware, so developers can tickle more performance out of the hardware available. This includes workarounds for bottlenecks. Nonetheless, such deep control does have its dangers, meaning developers need to know just exactly what they are doing, for example in memory management. The rather inconspicuous OpenGL API, at least compared to DirectX, is thus supposed to come to the fore a bit more.
The Vulkan API 1.0 is supported on Windows 7, Windows 8.1, Windows 10, Android and Linux. No specific games were announced, but the Games Developer Conference from 14 to 18 March in San Francisco could reveal more here. The Source 2 engine is so far the only known game engine, which has already installed the Vulkan API. Debugger from Valve, LunarG and Codeplay already are available to assist the debugging process.
The Khronos Group appears to be leading the developement of the Vulkan API, but AMD but is fare more than just a silent bystander. It therefore is of no surprise that the first beta driver was penned by the Radeon Technologies Group and is branded as "Radeon Software". Head of the Radeon Technologies Group is Raja Koduri.
A link to the documentation of the Vulkan API in version 1.0, the SDK and the driver can be found directly on AMD's site.