A survey article is presented which discusses the architecture of vector and parallel machines, the charcteristics of the machines that are currently available, and the computational gain that can be achieved using these new types of machine architectures. In addition, the literature and activities in the area of parallel computations in heat transfer and fluid flows are noted. To illustrate the high computing speeds that can be obtained on supercomputers, two heat transfer problems are solved on both scalar and vector machines. It is shown that the vectorized code executes two orders of magnitude faster on a supercomputer than the nonvectorized version on a standard, sequential mainframe computer.