Good computer architecture is, in many ways, very similar to good building architecture. Its effectiveness can only be judged by the way in which the implementation of the design - whether a computer or a building - fulfils its given role. In computer architecture, this judgement is based on one criterion - speed. In the best computers, speed is obtained by coupling the best current technology and materials with the best design. This Thesis presents a novel way in which to design pipelined computers. Speed is achieved by maximising the use of hardware resources to provide an environment in which many independent processes can execute concurrently in a single system. The design method is called context flow. Two different facets of context flow are discussed. An underlying theory of context flow is established which is used to prove certain properties of context flow systems. These theoretical results show context flow machines to be implementable. Using these results, a practical approach to the creation of context flow systems is presented, leading to the design and analysis of an example context flow processor. The result is an architectural design technique with a formal foundation which can be used to build efficient pipelined computers.