[en] A bow wave was previously observed in the solar wind upstream of each of the first six planets. The observed properties of these bow waves and the associated plasma flows are outlined, and those features identified that can be described by a continuum magnetohydrodynamic flow theory. An account of the fundamental concepts and current status of the magnetohydrodynamic and gas dynamic theories for solar wind flow past planetary bodies is provided. This includes a critical examination of: (1) the fundamental assumptions of the theories; (2) the various simplifying approximations introduced to obtain tractable mathematical problems; (3) the limitations they impose on the results; and (4) the relationship between the results of the simpler gas dynamic-frozen field theory and the more accurate but less completely worked out magnetohydrodynamic theory. Representative results of the various theories are presented and compared