The first next-gen, released graphics API was Mantle, which launched a little while after Battlefield 4, but the SDK is still invite-only. The DirectX 12 API quietly launched with the recent Windows 10 Technical Preview, but no drivers, SDK, or software (that we know about) are available to the public yet. The Khronos Group has announced their project, and that's about it currently.
According to Develop Magazine, the GDC event listing, and participants, the next OpenGL (currently called “glNext initiative”) will be unveiled at GDC 2015. The talk will be presented by Valve, but it will also include Epic Games, who was closely involved in DirectX 12 with Unreal Engine, Oxide Games and EA/DICE, who were early partners with AMD on Mantle, and Unity, who recently announced support for DirectX 12 when it launches with Windows 10. Basically, this GDC talk includes almost every software developer that came out in early support of either DirectX 12 or Mantle, plus Valve. Off the top of my head, I can only think of FutureMark as unlisted. On the other hand, while they will obviously have driver support from at least one graphics vendor, none are listed. Will we see NVIDIA? Intel? AMD? All of the above? We don't know.
When I last discussed the next OpenGL initiative, it was attempting to parse the naming survey to figure out bits of the technology itself. As it turns out, the talk claims to go deep into the API, with demos, examples, and “real-world applications running on glNext drivers and hardware”. If this information makes it out (and some talks remain private unfortunately although this one looks public) then we should know more about it than what we know about any competing API today. Personally, I am hoping that they spent a lot of effort on the GPGPU side of things, sort-of building graphics atop it rather than having them be two separate entities. This would be especially good if it could be sandboxed for web applications.
This could get interesting.