The lattice Boltzmann method has been established as an efficient technique for solving a wide range of complex problems in fluid dynamics including multiphase flows. In this paper, the extension of the technique to the simulation of non-Newtonian fluids is described. Two classes of non-Newtonian fluids are considered: inelastic fluids characterized by a variable viscosity and viscoelastic fluids characterized by fluid elasticity. A comprehensive review is given of developments in this area and sample numerical results are presented in the case of inelastic fluids.