The three main sections of this chapter deal with the ignition of flammable vapour/air mixtures, the ignition of liquids and the ignition of solids, respectively. The mechanism of autoignition of vapour/air mixtures is considered in some detail in Section 1. The section on the ignition of liquids concentrates on the concepts of flashpoint and firepoint, and the role of surface-tension-driven flows in the ignition of pools of high flashpoint liquids is discussed. Recent work on the autoignition of liquid fuels is reviewed. In the section on the ignition of solids, basic heat transfer theory is used to derive simple expressions for time to ignition at solid surfaces exposed to heat fluxes. Both piloted ignition and spontaneous ignition are considered and a clear distinction made between “thin” and “thick” solids. The importance of the physical properties of the solid and of the relevant environmental conditions are discussed. The chapter ends with a short review of the extinction of premixed and diffusion flames.