While we are all familiar with retaining information in a computer or our minds, memory is an essential quality of many more systems around us. Considering what a system remembers and what it must forget can reveal its non-equilibrium nature. In this talk, I focus on experiments with amorphous solids, and ordinary adhesive tape. They illustrate two generic, simple ways that a system can retain multiple values from a time-varying input—one widely studied, the other strangely obscure. Atop these general principles for classifying and designing matter with memory, the experiments also highlight some remarkable peculiarities of each material’s physics