View Activity Logs
"I have a student who says s/he took a quiz, but there's no sign of it in my course. How can I find out if s/he actually attempted to submit the quiz?"
This is a scenario that plays out frequently in my office. Fortunately, Moodle keeps track of everything everyone does in your course—including you! Read about activity logs here.
I took a quick screenshot of one of my courses as an example—my activity goes on for pages (!), but this will give you an idea of what you can find out about your learners' activities.