Parallelism is an intrinsic feature of many physical systems. The design of high-performance computers is increasingly making use of this concept by employing many processors working co-operatively to carry out a single computation. Consequently, the computer simulation of physical systems can rather naturally exploit the latest computer architectures to test theoretical models and to make measurements that are inaccessible to real experiments. In this article we review the design and use of parallel computers. In a subsequent article we will describe how they have been used to obtain insight into some fundamental problems in physics.