Even in the absence of turbulence, radiative heat transfer has important influences on the global and local behavior of flames. There is a large and rapidly growing body of literature containing analytic, experimental and simulation studies aimed at isolating and quantifying the influences of radiation on (for example) laminar flame speeds and pollutant emissions in laminar flames. Radiation plays an especially prominent role in “threshold” phenomena, including flammability, extinction, and stability limits for laminar flames. These effects can be amplified in turbulent flames. In this chapter, several examples of important radiation effects in laminar and transitional flames are discussed, before returning to the fully turbulent flames that are the primary focus of this monograph. Spatially one-dimensional systems are considered first, followed by two-dimensional systems. Examples are provided for both premixed and nonpremixed flames.