Modern computing, as well as the historical development of computing, has been dominated by sequential monoprocessing. Yet there is the alternative of parallelism, where several processes may be in concurrent execution. This alternative is discussed, in which the main developments involving parallelism are considered both from the standpoint of computing systems and that of applications than can exploit such systems. The account seeks to treat parallelism in a historical context, and to identify all the main aspects of concurrency in computation right up to the present time. The review includes a discussion both of parallel computer architectures and functional units as components in these architectures. The important question of limitations in concurrency is considered, and there is an account of typical numerical problems which contain parallelism, as well as languages appropriate to code these problems. Included will be a brief consideration of what use parallelism might be In the field of data processing.