Simulation of heterogeneous reservoirs can require distorted grids to give an accurate model of the reservoir geology with a moderate number of grid cells. In this paper we study grid construction in which grid lines are encouraged to follow either the boundaries between different rock types or regions of different permeability. An algorithm is described which finds a global near-optimal solution, to such problems. We find that, even with grid controls, good grids can depart from orthogonality. The final part of the paper therefore considers the problem of discretisation on near-orthogonal grids. We describe a mixed finite element approach which is a natural and compact generalisation of the standard block-centred finite difference method.