Most toolkits have an event loop (built above some multiplexing syscall like poll(2) -or the obsolete select
-...), e.g. GTK has g_application_run (which is above:) gtk_main which is built above Glib main event loop (which in fact does a poll
or something similar). Likewise, Qt has QApplication and its exec methods.
Very often, you can register timers within the event loop. For GTK, use GTimers, g_timeout_add etc. For Qt learn about its timers.
Very often, you can also register some idle or background processing, which is one of your function which is started by the event loop after other events and timeouts have been processed. Your idle function is expected to run quickly (usually it does a small step of some computation in a few milliseconds, to keep the GUI responsive). For GTK, use g_idle_add etc. IIRC, in Qt you can use a timer with a 0 delay.
So you could code even a (conceptually) single threaded application, using timeouts and idle processing.
Of course, you could use multi-threading: generally the main thread is running the event loop, and other threads can do other things. You have synchronization issues. On POSIX systems, a nice synchronization trick could be to use a pipe(7) to self: you set up a pipe before running the event loop, and your computation threads may write a few bytes on it, while the main event loop is "listening" on it (with GTK, using g_source_add_poll or async IO or GUnixInputStream etc.., with Qt, using QSocketNotifier etc....). Then, in the input handler running in the main loop for that pipe, you could access traditional global data with mutexes etc...
Conceptually, read about continuations. It is a relevant notion.