Accidental non-stationary combustion processes are the main issue of safety considerations in connection with hydrogen technology. The overpressure loads produced by detonations but as well those imposed upon structures by fast, turbulent deflagrations are easily of sufficient strength for serious damage. Since an accidental combustion process is most likely to start as a slow deflagration, detailed knowledge of the mecbanisms of flame acceleration leading to high-speed reaction fronts is of vital importance for design guidelines and safety analysis. In this paper the parameters influencing turbulent flame acceleration processes, i.e. initial conditions and geometry of the combustion volume, are discussed and a brief outlook for necessary future research activities is provided.