We discuss the Lattice Boltzmann method (LBM), which provides a new way of thinking on complex, multiphase fluid flow problems. We present the basics of the LBM as well as its origins in the Cellular Automata. The particle-based nature of the LBM makes it well suited to study fluid-boundary interfaces. We then commence to sketch advanced applications like particle suspension problems and we show how the LBM can be applied on turbidity currents, a challenging fluid flow problem. We show that the LBM has a good deal of versatility in modeling physical systems.