During the past several years, a great number of proposals have been made with the objective to increase supercomputer performance by an order of magnitude on the basis of a utilization of new computer architectures. The present paper is concerned with a suitable classification scheme for comparing these architectures. It is pointed out that there are basically four schools of thought as to the most important factor for an enhancement of computer performance. According to one school, the development of faster circuits will make it possible to retain present architectures, except, possibly, for a mechanism providing synchronization of parallel processes. A second school assigns priority to the optimization and vectorization of compilers, which will detect parallelism and help users to write better parallel programs. A third school believes in the predominant importance of new parallel algorithms, while the fourth school supports new models of computation. The merits of the four approaches are critically evaluated. 50 references.