Linux kernel and glibc

I have this question for a while. What's the dependency of kernel and system libraries such as glibc? Can kernel codes call functions in glibc? Do we need glibc when we compile kernel? Or do we need kernel code to compile glibc?

This is what I found from http://kernelnewbies.org/FAQ/LibraryFunctionsInKernel:

Q: Can I use library functions in the kernel ?
A: System libraries (such as glibc, libreadline, libproplist, whatever) that are typically available to userspace programmers are unavailable to kernel programmers. When a process is being loaded the loader will automatically load any dependent libraries into the address space of the process. None of this mechanism is available to kernel programmers: forget about ISO C libraries, the only things available is what is already implemented (and exported) in the kernel and what you can implement yourself.

Note that it is possible to "convert" libraries to work in the kernel; however, they won't fit well, the process is tedious and error-prone, and there might be significant problems with stack handling (the kernel is limited to a small amount of stack space, while userspace programs don't have this limitation) causing random memory corruption.

Many of the commonly requested functions have already been implemented in the kernel, sometimes in "lightweight" versions that aren't as featureful as their userland counterparts. Be sure to grep the headers for any functions you might be able to use before writing your own version from scratch. Some of the most commonly used ones are in include/linux/string.h.

Whenever you feel you need a library function, you should consider your design, and ask yourself if you could move some or all the code into user-space instead.

So, the idea is that the kernel doesn't (and actually can't) refer to external libraries. Kernel and glibc can be compiled seperately. However, glibc seems to have to compile against a particular kernel. Why? because it uses some kernel headers. Also, when a new kernel comes out, it's new features can't be handles by the old APIs, new libraries are needed and they have to be compiled against the new kernel.