Agreement about planetary formation processes deteriorates sharply with distance from the Sun. While the terrestrial planets are widely believed to have formed from the collisional accumulation of solid bodies, there are two competing mechanisms for the formation of the gas giant planets, basically 'bottom-up' or 'top-down'. The former is the traditional core accretion mechanism, where a roughly 10 Earth-mass solid core forms by collisional accumulation, followed by hydrodynamic accretion of a gaseous envelope. The latter is the recently revived disk instability mechanism, where a protoplanetary disk forms self-gravitating protoplanets through a gravitational instability of the gaseous disk, followed by settling and coagulation of dust grains to form central solid cores. These same two mechanisms have been modified to explain the formation of the ice giant planets. Their solid cores are thought to form too slowly to accrete substantial gaseous envelopes prior to disk removal in the core accretion mechanism, while in the disk instability mechanism, radiation from nearby massive stars is hypothesized to remove most of the protoplanets' gaseous envelopes following core formation. Both of these mechanisms for gas and ice giant planet formation have a number of advantages and disadvantages, making a purely theoretical choice between them challenging. However, the ongoing discovery of extrasolar planetary systems promises to provide considerable insight into which of these mechanisms is responsible for forming most gas and ice giant planets in the galaxy, and by inference, those in our own Solar System.