The availability of parallel processing hardware and software presents an opportunity and a challenge to apply this new computation technology to solve power system problems. The allure of parallel processing is that this technology has the potential to be cost effectively used on computationally intense problems. The objective of this paper is to define the state of the art and identify what the authors see to be the most fertile grounds for future research in parallel processing as applied to power system computation. As always, such projections are risky in a fast changing field, but the authors hope that this paper will be useful to the researchers and practitioners in this growing area.