Thin film coating flows have many environmental, medical and scientific applications and are ubiquitous throughout the chemical engineering industry. Examples range from photolithographic manufacture of microelectronic components via centrifugally-driven flow over patterned substrates to the more traditional gravity-driven slide coating flows popular in the photographic industry. The accurate numerical simulation of such flows, which are often fully three-dimensional and/or composed of several liquid layers, is enormously challenging. This paper briefly reviews current capabilities and limitations of existing numerical techniques and presents a range of new results which highlight the applicability of lubrication, Finite Element and lattice Boltzmann-based methods for coating flows and future developments needed to improve their utility in industrial design.