We use the lattice Boltzmann algorithm as a tool to investigate the hydrodynamic properties of complex fluids. As a first example we consider a strongly non-Newtonian fluid, cholesteric liquid crystals. When these are forced along a direction parallel to the helical axis the apparent viscosity increases by several orders of magnitude. We explain some puzzles in the Helfrich theory of this effect. We then investigate the dynamics of micron-scale droplets spreading on chemically and topologically patterned substrates. For a substrate with lyophobic and lyophilic stripes of the same dimensions as the drop the final droplet shape is determined by the dynamic evolution of the fluid. For a substrate patterned with posts the substrate becomes superhydrophobic -- like the back of the Nambian desert beetle.