This special issue is dedicated to Professor Moshe Matalon on the occasion of his 70th birthday, as a tribute to his outstanding contributions to Combustion Theory and Fluid Mechanics and for his leadership and dedication to Combustion Theory and Modelling since its inception in 1996. Moshe has make significant and long lasting contributions to the development of consistent mathematical theories explaining the interrelation between fluid mechanics and combustion by employing rigorous asymptotic methods and careful numerical simulations in many configurations over the last 44 years. This includes the formulation of hydrodynamic theory of premixed flames, the derivation of an invariant formula for the flame-stretch rate, and the characterisation of thermo-diffusive instabilities in non-premixed flames, among others contributions. The papers collected in this issue by friends and colleagues of Moshe represent a snapshot of his research philosophy, that combines theoretical and numerical studies to aid in the interpretation of experimental results, to advance understanding and to push the frontiers of combustion modelling development and their use in practice.