There are five individually plausible and jointly incompatible assumptions underlying four familiar puzzles about material constitution. The problem of material constitution just is the fact that these five assumptions are both plausible and incompatible. I will begin by providing a very general statement of the problem. I will present the five assumptions and provide a short argument showing how they conflict with one another. Then, in subsequent sections, I will go on to show how these assumptions underlie each of the (...) four puzzles. I will conclude by providing an exhaustive taxonomy of possible solutions to the problem. (shrink)