Abstract Accidental explosions of flammable gases and reactive gas mixtures remain a significant concern in process industries. The present paper reviews the basic mechanism of Flame Acceleration (FA), the results of recent studies on FA, and their application to explosion safety. A short overview of the physical phenomena involved in FA is followed by the description of FA and flame propagation regimes in smooth tubes, obstructed channels, unconfined and semi-confined mixtures with or without congestion. A framework is summarized that may be used to evaluate the potential for FA and the onset of detonation. Advances made over recent years in the understanding of FA are discussed. These advances include: new theoretical models that address various aspects of the phenomena involved in FA, high resolution numerical simulations and new detailed experimental studies. A combination of the results of these studies is shown to allow for a significant improvement of our ability to address practical problems. Areas where additional research is required to improve reliability of predictions of FA for industrial safety applications are also discussed.