We discuss a novel approach to compute the radiative lifetime (RL) of charge carriers and excitons. The calculations employ the GW-BSE method to obtain the exciton dipole matrix elements, which are then combined with Fermi's golden rule to obtain the zero-temperature RLs. Temperature-dependent RLs are then computed by averaging over center-of-mass momenta (at low temperature) and also over excitonic states at room temperature. Derivations of the RLs for 1D, 2D, and bulk materials are presented, together with applications to materials for lighting, including 2D transition metal dichalcogenides and bulk GaN and InGaN, and for solar cells, including lead-iodide perovskites. Comparison of the computed RLs with time-resolved photoluminescence experiments is discussed. The technical challenges toward obtaining the quantum yield and carrier diffusion lengths from first principles are outlined.