Abstract: Spatial-temporal evolution of a thin film falling along aninclined plane is always a hot issue in the study of hydrodynamics. Thispaper reviews the development of falling films from the long-waveapproximation equation to the integral boundary layer equation, from thelinear instability analysis to the weakly nonlinear analysis, from the primaryinstability to the secondary instability and from the finite amplitudecomputation to the direct numerical simulation. The maintheoretical and experimental results of falling films are summarized. Recent progresses onthe heated falling film are also introduced, together with other typesof falling films.