When dealing with thin layer flow, a key technique is the well-known lubrication theory. It is shown how the lubrication approximation is achieved through a systematic reduction of the Navier-Stokes equations. Subsequently, the equations are applied to channel and free surface flows. The channel flow version is employed to model solidification in a microchannel with a flowing fluid (in the context of phase change microvalves) and also contact melting. Aircraft ice accretion is an infamous problem in the aviation industry. The mathematical model is analogous to ice growth on any structure, such as wind turbines, power cables, structures, and ships. The final sections deal with solidification in the presence of a moving thin fluid layer with a free surface (in the context of in-flight aircraft ice accretion) as well as a recent modification for ice crystal icing, which involves the enthalpy formulation.