Should I use std::function or a function pointer in C++?

In short, use std::function unless you have a reason not to.

Function pointers have the disadvantage of not being able to capture some context. You won't be able to for example pass a lambda function as a callback which captures some context variables (but it will work if it doesn't capture any). Calling a member variable of an object (i.e. non-static) is thus also not possible, since the object (this-pointer) needs to be captured.⁽¹⁾

std::function (since C++11) is primarily to store a function (passing it around doesn't require it to be stored). Hence if you want to store the callback for example in a member variable, it's probably your best choice. But also if you don't store it, it's a good "first choice" although it has the disadvantage of introducing some (very small) overhead when being called (so in a very performance-critical situation it might be a problem but in most it should not). It is very "universal": if you care a lot about consistent and readable code as well as don't want to think about every choice you make (i.e. want to keep it simple), use std::function for every function you pass around.

Think about a third option: If you're about to implement a small function which then reports something via the provided callback function, consider a template parameter, which can then be any callable object, i.e. a function pointer, a functor, a lambda, a std::function, ... Drawback here is that your (outer) function becomes a template and hence needs to be implemented in the header. On the other hand you get the advantage that the call to the callback can be inlined, as the client code of your (outer) function "sees" the call to the callback will the exact type information being available.

Example for the version with the template parameter (write & instead of && for pre-C++11):

template <typename CallbackFunction>
void myFunction(..., CallbackFunction && callback) {
    ...
    callback(...);
    ...
}

As you can see in the following table, all of them have their advantages and disadvantages:

_{(1) Workarounds exist to overcome this limitation, for example passing the additional data as further parameters to your (outer) function: myFunction(..., callback, data) will call callback(data). That's the C-style "callback with arguments", which is possible in C++ (and by the way heavily used in the WIN32 API) but should be avoided because we have better options in C++.}

_{(2) Unless we're talking about a class template, i.e. the class in which you store the function is a template. But that would mean that on the client side the type of the function decides the type of the object which stores the callback, which is almost never an option for actual use cases.}

_{(3) For pre-C++11, use boost::function}

void (*callbackFunc)(int); may be a C style callback function, but it is a horribly unusable one of poor design.

A well designed C style callback looks like void (*callbackFunc)(void*, int); -- it has a void* to allow the code that does the callback to maintain state beyond the function. Not doing this forces the caller to store state globally, which is impolite.

std::function< int(int) > ends up being slightly more expensive than int(*)(void*, int) invocation in most implementations. It is however harder for some compilers to inline. There are std::function clone implementations that rival function pointer invocation overheads (see 'fastest possible delegates' etc) that may make their way into libraries.

Now, clients of a callback system often need to set up resources and dispose of them when the callback is created and removed, and to be aware of the lifetime of the callback. void(*callback)(void*, int) does not provide this.

Sometimes this is available via code structure (the callback has limited lifetime) or through other mechanisms (unregister callbacks and the like).

std::function provides a means for limited lifetime management (the last copy of the object goes away when it is forgotten).

In general, I'd use a std::function unless performance concerns manifest. If they did, I'd first look for structural changes (instead of a per-pixel callback, how about generating a scanline processor based off of the lambda you pass me? which should be enough to reduce function-call overhead to trivial levels.). Then, if it persists, I'd write a delegate based off fastest possible delegates, and see if the performance problem goes away.

I would mostly only use function pointers for legacy APIs, or for creating C interfaces for communicating between different compilers generated code. I have also used them as internal implementation details when I am implementing jump tables, type erasure, etc: when I am both producing and consuming it, and am not exposing it externally for any client code to use, and function pointers do all I need.

Note that you can write wrappers that turn a std::function<int(int)> into a int(void*,int) style callback, assuming there are proper callback lifetime management infrastructure. So as a smoke test for any C-style callback lifetime management system, I'd make sure that wrapping a std::function works reasonably well.

Use std::function to store arbitrary callable objects. It allows the user to provide whatever context is needed for the callback; a plain function pointer does not.

If you do need to use plain function pointers for some reason (perhaps because you want a C-compatible API), then you should add a void * user_context argument so it's at least possible (albeit inconvenient) for it to access state that's not directly passed to the function.

The only reason to avoid std::function is support of legacy compilers that lack support for this template, which has been introduced in C++11.

If supporting pre-C++11 language is not a requirement, using std::function gives your callers more choice in implementing the callback, making it a better option compared to "plain" function pointers. It offers the users of your API more choice, while abstracting out the specifics of their implementation for your code that performs the callback.