Implementations

Compiler toolchains generate and read ELF files.

Sane compilers should use a separate standalone library to do the dirty work. E.g., Binutils uses BFD (in-tree and canonical source).

Operating systems read and run ELF files.

Kernels cannot link to a library nor use the C stlib, so they are more likely to implement it themselves.

This is the case of the Linux kernel 4.2 which implements it in th file fs/binfmt_elf.c.