This talk describes a new approach for large-scale computational problems which is particularly effective when a relatively simple algorithm is used. We demonstrate that it is possible to design and construct, at modest cost, special purpose computers for various classes of problems. By exploiting the principles of pipelining and parallel processing, and by adapting the hardware design to the specific structure of a particular algorithm, one can obtain a device which is as fast as or faster than general-purpose commercial supercomputers. The user of a such a processor has the double advantage of its speed and of its continuous availability for the particular problem for which it was constructed. In statistical mechanics special purpose computers have been built recently (i) for Monte Carlo simulation of the lsing model, and (ii) for the molecular dynamics of classical many-particle systems with short-range interactions: The design and performance of these machines are discussed and compared to those of commercial computers.