At the suggestion of the Editor-in-Chief, Dr. N.K. Bose, we invited various researchers to contribute to a special issue which focused on the use of optical hardware and methods to solve multidimensional signal processing tasks. This special issue contains papers which span a range of applications of optics to signal processing. Optics here refers to the imposition of information on a two dimensional wavefront and the modulation of this information by the optical processor. The intrinsic parallelism of optics suggests very high computational throughputs provided the information to be processed can be read onto and read from the propagating wavefront sufficiently rapidly. The first paper, by Fiddy, entitled “Multidimensional Processing: Nonlinear Optics and Computing,” describes some of the background to the use of optics in this context. It is primarily written for the nonspecialist in optical processing and reviews some of the potential advantages and prospects for optical processing and computing. This tutorial paper discusses both the needs of computing and the developing optical hardware and materials required. The second paper, by John Caulfield, takes a very fundamental look at the “in principle” advantages one can expect from an optical processing system. It is entitled “Space-time Complexity in Optical Computing” and describes how the spatial and temporal complexity of the computing hardware is related to the complexity of the problem. In particular, the possibility of performing a “fan-in” of data optically leads to computational advantages not realizable by nonoptical means.