Trouble staying asleep is more common than trouble falling asleep, and it gets written about far less. The pattern is familiar to anyone who has it: asleep without much difficulty, awake at two or three, and then a stretch of lying there while the mind starts working.
Waking in the night is not itself a problem. Everyone surfaces briefly several times a night at the end of each sleep cycle, and normally rolls over without ever registering it. What turns a normal wake into an hour of lying awake is what happens next — checking the clock, working out how much is left, deciding tomorrow is ruined. The arousal that follows is the thing keeping you up, not the wake that started it.
These articles cover what is happening physiologically, what to do at three in the morning when it is happening, and the signs that point to something other than insomnia and are worth taking to a doctor.