We develop a comprehensive three-dimensional (3D) model of gas generation and transport in landfills. The model, which is developed for a four-component gas mixture, takes into account the effect of heterogeneity in the distributions of the permeability and porosity in the landfill, as well as that of the soil that surrounds it. It also takes into account the presence of an arbitrary number of gas extraction wells with an arbitrary spatial distribution. The governing non-linear equations of mass transport and reaction are solved by a novel iterative method that bypasses the non-linearity without making any approximation. The model is utilized for investigating gas generation and transport in a model landfill, and the effect of various parameters that control these phenomena.