In many important combustion applications, heat transfer is dominated by thermal radiation from combustion gases and soot. Thermal radiation from combustion gases is extremely complicated, and accurate and efficient predictions are only now becoming possible with the use of accurate global methods, such as full-spectrum k-distributions, and with state-of-the-art line-by-line accurate Monte Carlo methods. The coupling between turbulence and radiation can more than double the radiative loss from a flame, while making theoretical predictions vastly more complicated. This paper is an embellished version of the 2021 Max Jakob Award lecture: Radiative properties and computational methods will be briefly discussed, and several examples of turbulent reacting flows, an oxy-fuel furnace, and high-pressure fuel sprays in combustion engines will be presented. Thermal radiation can also be used as an optical diagnostic tool to determine temperature and concentration distributions, which will be briefly discussed.