We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In addition, working in (0 + 1) dimensions considerably simplifies the mathematics, allowing the physical concepts involved to be exhibited more clearly. (Contains 17 footnotes and 4 figures.)