An interleaver is a hardware device commonly used in conjunction with error correcting codes to counteract the effect of burst errors. Interleavers are in widespread use and much is known about them from an engineering standpoint. In this paper we propose a mathematical model that provides a rigorous foundation for the theoretical study of interleavers. The model captures precisely such notions as block and convolutional interleavers, spread, periodicity, causality, latency, and memory usage. Using this model, we derive several optimality results on the latency and memory usage of interleavers. We describe a family of block interleavers and show that they are optimal with respect to latency among all block interleavers with a given spread. We also give tight upper and lower bounds on the memory requirements of interleavers.