Abstract We present a surface-based approach to reservoir model construction in which all geological heterogeneity, whether structural, stratigraphic, sedimentological or diagenetic, that impacts on the spatial distribution of petrophysical properties is modelled as one or more discrete volumes bounded by surfaces. The modelled surfaces can be deterministically interpolated between control lines or points, or incorporate a stochastic element where control data are sparse. Models constructed from surfaces are not constrained by an underlying grid; indeed, the model is generated without reference to a grid. The only difference between ‘geological’ and ‘simulation’ models is that the latter incorporates a grid or mesh to allow numerical solution of the governing flow equations, the architecture of which is driven by the architecture of the modelled surfaces. This approach to gridding (or meshing) is directly compatible with the next generation of unstructured-mesh simulators, and allows the capabilities of the latter to be utilized fully in the modelling of complex reservoir architectures. A surface-based approach to model construction may facilitate a step change in reservoir modelling capabilities: once the requirement to upscale geological models to a structured simulation grid is removed, there is no need to build geological models that are restricted by grid resolution.