Which registers must be preserved across function calls (callee-saved vs. caller-saved)?

Callee-saved registers (%rbx, %rbp, %r12–%r15) must survive a call — the called function saves and restores them; caller-saved registers may be freely clobbered.

* Callee-saved registers (%rbx, %rbp, %r12-%r15) must be preserved by the called function; caller-saved ones may be clobbered, so the caller saves what it still needs. *

The calling convention splits the registers so that the caller and callee don't both try to use the same one and corrupt each other. The deal is:

What it means in practice:

• Callee-saved: if a function wants to use %rbx, it must push it on entry and pop it before returning, leaving it as it found it.
• Caller-saved: if you have a value in %rax that you need after a call, you must save it first, because the callee is allowed to trash it.

my_func:
    push %rbx            # save callee-saved register
    mov  %rdi, %rbx      # now safe to use %rbx
    call other_func      # %rbx is preserved across this call
    mov  %rbx, %rax
    pop  %rbx            # restore before returning
    ret

Go deeper:

• x86 calling conventions (Wikipedia) — the callee-saved vs caller-saved register split of the System V ABI.