In this paper, I review the literature on the use of garbage collection in real-time systems. I concentrate on hard real-time systems, where we ideally construct mathematical proofs of correctness and of timing properties. In particular, I examine the interaction of overheads imposed on mutator operations by garbage collection algorithms on worst-case execution time analyses of real-time threads performing those operations. In recent years there has been a shift from work-based to time-based approaches. This paper explains and motivates this shift, and reviews examples, problems, and advantages of example algorithms from each approach. Finally, I examine what extensions to programming verification technology might be necessary to prove that sufficient memory space exists to run a real-time system with the same rigor that one proves that sufficient time exists in a real-time schedule.