This paper looks at Ya.B. Zeldovich’s ideas on the combustion and detonation physics of gas mixtures and how they evolved as work in this field progressed. The paper demonstrates the fundamental role of Zeldovich’s concept of spontaneous combustion wave in studying transient initiation processes for various combustion regimes and in determining the energy and concentration inflammation limits for combustible gas mixtures. It shows how his notion that flame front stretching crucially influences flame acceleration in channels explains in a new way the deflagration-to-detonation transition in highly reactive gaseous mixtures. Most of the presented results were obtained by simulation, allowing Zeldovich’s ideas to be extended to the combustion of real gaseous mixtures, where chemical reactions and gasdynamical flows add hugely to the complexity of the problem. The paper concludes by using Zeldovich’s mechanism to assess the amount of nitrogen oxide produced by a lightning discharge.