How should a function accept a function parameter in terms of constness and referenceness?

How do each of the following behave differently? I'm unclear what effect const has on the function parameter, and what the difference in this case would be between passing by value, by reference, or by rvalue reference. Which one of these is "best"?

#include <functional>

void foo_with_func(      std::function<void()>   f) { ...; f(); ...; }
void foo_with_func(      std::function<void()>&  f) { ...; f(); ...; }
void foo_with_func(      std::function<void()>&& f) { ...; f(); ...; }
void foo_with_func(const std::function<void()>   f) { ...; f(); ...; }
void foo_with_func(const std::function<void()>&  f) { ...; f(); ...; }
void foo_with_func(const std::function<void()>&& f) { ...; f(); ...; }