If you're in the "we don't use exceptions" camp, then how do you use the standard library?

I will answer for myself and my corner of the world. I write c++14 (will be 17 once compilers have better support) latency critical financial apps that process gargantuan amounts of money and can't ever go down. The ruleset is:

• no exceptions
• no rtti
• no runtime dispatch
• (almost) no inheritance

Memory is pooled and pre-allocated, so there are no malloc calls after initialization. Data structures are either immortal or trivially copiable, so destructors are nearly absent (there are some exceptions, such as scope guards). Basically, we are doing C + type safety + templates + lambdas. Of course, exceptions are disabled via the compiler switch. As for the STL, the good parts of it (i.e.: algorithm, numeric, type_traits, iterator, atomic, ...) are all useable. The exception-throwing parts coincide with the runtime-memory-allocating parts and the semi-OO parts nicely so we get to get rid of all the cruft in one go: streams, containers except std::array, std::string.

Why do this?

1. Because like OO, exception offers illusory cleanliness by hiding or moving the problem elsewhere, and makes the rest of the program harder to diagnose. When you compile without "-fno-exceptions", all your clean and nicely behaved functions have to endure the suspicion of being failable. It is much easier to have extensive sanity checking around the perimeter of your codebase, than to make every operation failable.
2. Because exceptions are basically long range GOTOs that have an unspecified destination. You won't use longjmp(), but exceptions are arguably much worse.
3. Because error codes are superior. You can use [[nodiscard]] to force calling code to check.
4. Because exception hierarchies are unnecessary. Most of the time it makes little sense to distinguish what errored, and when it does, it's likely because different errors require different clean-up and it would have been much better to signal explicitly.
5. Because we have complex invariants to maintain. This means that there are code, however deep down in the bowels, that need to have transnational guarantees. There are two ways of doing this: either you make your imperative procedures as pure as possible (i.e.: make sure you never fail), or you have immutable data structures (i.e.: make failure recovery possible). If you have immutable data structures, then of course you can have exceptions, but you won't be using them because when you will be using sum types. Functional data structures are slow though, so the other alternative is to have pure functions and do it in an exception-free language such as C, no-except C++, or Rust. No matter how pretty D looks, as long as it isn't cleansed of GC and exceptions, it's an non-option.
6. Do you ever test your exceptions like you would an explicit code path? What about exceptions that "can never happen"? Of course you don't, and when you actually hit those exceptions you are screwed.
7. I have seen some "beautiful" exception-neutral code in C++. That is, it performs optimally with no edge cases regardless of whether the code it calls uses exceptions or not. They are really hard to write and I suspect, tricky to modify if you want to maintain all your exception guarantees. However, I have not seen any "beautiful" code that either throws or catches exceptions. All code that I have seen that interacts with exceptions directly have been universally ugly. The amount of effort that went into writing exception-neutral code completely dwarfs the amount of effort that was saved from the crappy code that either throws or catches exceptions. "Beautiful" is in quotes because it is not actual beauty: it is usually fossilized because editing it requires the extra burden of maintaining exception-neutrality. If you don't have unit tests that deliberately and comprehensively misuse exceptions to trigger those edge cases, even "beautiful" exception-neutral code decays into manure.

In our case, we disable the exceptions via the compiler (e.g -fno-exceptions for gcc).

In the case of gcc, they use a macro called _GLIBCXX_THROW_OR_ABORT which is defined as

#ifndef _GLIBCXX_THROW_OR_ABORT
# if __cpp_exceptions
#  define _GLIBCXX_THROW_OR_ABORT(_EXC) (throw (_EXC))
# else
#  define _GLIBCXX_THROW_OR_ABORT(_EXC) (__builtin_abort())
# endif
#endif

(you can find it in libstdc++-v3/include/bits/c++config on latest gcc versions).

Then you juste have to deal with the fact that exceptions thrown just abort. You can still catch the signal and print the stack (there is a good answer on SO that explains this), but you have better avoid this kind of things to happen (at least in releases).

If you want some example, instead of having something like

try {
   Foo foo = mymap.at("foo");
   // ...
} catch (std::exception& e) {}

you can do

auto it = mymap.find("foo");
if (it != mymap.end()) {
    Foo foo = it->second;
    // ...
}

I also want to point out, that when asking about not using exceptions, there's a more general question about standard library: Are you using standard library when you're in one of the "we don't use exceptions" camps?

Standard library is heavy. In some "we don't use exceptions" camps, like many GameDev companies for example, better suited alternatives for STL are used - mostly based on EASTL or TTL. These libraries don't use exceptions anyway and that's because eighth generation consoles didn't handle them too well (or even at all). For a cutting edge AAA production code, exceptions are too heavy anyway, so it's a win - win scenario in such cases.

In other words, for many programmers, turning exceptions off goes in pair with not using STL at all.