I understand there's an openCL C++ API, but I'm having trouble compiling my kernels... do the kernels have to be written in C? And then it's just the host code that's allowed to be written in C++? Or is there some way to write the kernels in C++ that I'm not finding? Specifically, I'm trying to compile my kernels using pyopencl, and it seems to be failing because it's compiling them as C code.
OpenCL C is a subset of C99.
There is also OpenCL C++ (OpenCL 2.1 and OpenCL 2.2 specs) which is a subset of C++14 but it's not implemented by any vendor yet (OpenCL 2.1 partially implemented by Intel but not C++ kernels).
Host code can be written in C,C++,python, etc.
In short you can read about OpenCL on wikipedia. There is a description about each OpenCL version. In pyopencl you can use OpenCL1.2 (as far as I'm aware there isn't support for OpenCL2.0 yet).
More details about OpenCL on Khronos website.