A falling liquid film is an open-flow hydrodynamic system that is convectively unstable to long-wave perturbations and exhibits a rich variety of spatiotemporal structures, which is found in a wide spectrum of engineering applications, such as evaporators, heat exchangers and chemical reactor columns. At low frequencies, long-wave perturbations to falling liquid films with sufficiently high Reynolds number evolve into fast moving solitary waves. These solitary waves are characterised by a dominant elevation with a long tail and a steep front, typically with capillary ripples preceding the main wave hump. Although the flow in the considered liquid films is laminar, the velocity profile in the solitary wave can be strongly non-parabolic, including flow recirculation and flow reversal, which for instance improves the heat and mass transfer in the liquid film. This seminar focuses on the basic hydrodynamic interactions that govern such solitary waves, based on results of direct numerical simulations and laboratory experiments. By applying simple hydrodynamic scaling arguments, a self-similar characterisation of the wave shape and wave speed for inertia-dominated solitary waves is derived that unveils the fundamental hydrodynamic interactions. The presented hydrodynamic arguments are then extended to elucidate how flow recirculation reduces the effective inertia acting on the wave to stabilise the wave height and how capillary ripples increase the stability of the solitary wave.