Which C/C++ compiler does Xcode use?

For C++:

Xcode 4.6.2 uses the Clang C++ compiler frontend with LLVM as backend which is conform to the C++11 standart and uses libc++ as the standart library.

Here you can finde a apple presentation about libc++.

I'm not an XCode user, but it seems to be Apple's LLVM Compiler (by default) according to Apple's website: https://developer.apple.com/technologies/tools/. But, I guess, like any other IDE XCode does support other compilers like GCC. Also depends on your XCode version it seems: http://useyourloaf.com/blog/2011/03/21/compiler-options-in-xcode-gcc-or-llvm.html

Here's a question in SO that asks about the default compiler and the answer seems to have the code to find just that: In Xcode 4.5, what is "Compiler Default" for "C++ Standard Library" and "C++ Language Dialect"?

According to this post 4.6 uses clang instead of GCC for C++: http://cplusplusmusings.wordpress.com/2013/02/26/c-and-xcode-4-6/

P.S.: Googling does help ;)

I just noticed the second half of the question was never really answered:

... I'd like to know where I can find the API documentation of the respective standard library ...

A simple Google search will reveal a wealth of information about this. Do note, however, that the "C++ Standard Library" is not the same thing as the "C Standard Library," so be careful of that when searching and reading. C++ has its roots in C, but the two have diverged to become separate languages that share a lot of commonality -- and a lot of hidden differences.

The canonical reference work regarding this is titled, appropriately enough, "The C++ Standard Library" by Nicolai M. Josuttis, published by Addison-Wesley. Many C++ programmers keep this on their bookshelves as a reference.

There is a good online reference for the library at https://cppreference.com/.

If you are interested in specifics of the LLVM implementation used by Apple's Xcode, see https://libcxx.llvm.org/ .

For a comprehensive list of the most highly recommended books and references for C++, Stack Overflow already has a very good FAQ regarding this: The Definitive C++ Book Guide and List.