New developments related partly to the increasing availability of high-performance, 32-bit microprocessors favor the design of high-performance computing systems made of high-volume, low-cost components. The present paper provides an evaluation of the state of the art regarding multiprocessing and indicates some major research problems which must be solved before VLSI multiprocessors and parallel processors will become commonplace. Attention is given to throughput-oriented multiprocessing, high-availability multiprocessing, response-oriented multiprocessing, parallel processing research problems, and future directions. Intrinsically parallel applications are considered along with parallel algorithms, parallel models of computation, parallel programming languages, and novel programming languages. 23 references.