The dissociation probability of CH4 on metal surfaces displays striking, interrelated dependencies on several parameters such as the incident kinetic energy (or the gas-temperature) and the surface temperature, as well as a large CH4/CD4 isotope effect. Many models have been proposed to account for one aspect or another of this behavior, but none has yet succeeded in explaining all aspects in a coherent way. In this paper we will show that all experimental results to date are consistent with a mechanism based on a concerted direct dissociation breaking a single CH bond on impact. A theoretical model describing this mechanism is developed by treating nuclear dynamics on a reasonable reduced dimensionality potential energy surface, with the CH4 or CD4 behaving essentially like a quasidiatomic molecule RH. We demonstrate explicitly that this dissociation mechanism is dominated by quantum mechanical tunneling. We resolve previous controversies about tunneling models by showing that the tunnel process cannot be viewed in terms of a static one-dimensional barrier, but must be interpreted as a quantum dynamics problem involving a potential energy surface with a minimum of three degrees of freedom; the distance of the molecule to the surface Z, the RH bond distance D and a coordinate representing lattice vibrations. In particular, a dynamic coupling to the lattice during the tunneling process is a crucial element and gives rise to the phenomenon of thermally assisted tunneling, which dominates the rate of dissociation under conditions that obtain in all experiments and in industrial catalysis. Via explicit quantum dynamical calculations using a model interaction we show that a wide variety of results from previous molecular beam and thermal "activation" experiments can readily be understood, in many cases semi-quantitatively. Since this model explains satisfactorily the full range of dramatic interrelated dependencies on controllable parameters for CH4 and CD4 dissociation on metals, we believe the basic mechanism whereby this important dissociation reaction occurs to be established. © 1991.