Light emission in two-dimensional (2D) transition metal dichalcogenides (TMDs) changes significantly with number of layers and stacking sequence. While the electronic structure and optical absorption are well understood in 2Dï¿½TMDs, much less is known about exciton dynamics and radiative recombination. In this talk, we show first principles calculations of intrinsic exciton radiative lifetimes at low temperature (4 K) and room temperature (300 K) in TMD monolayers with chemical formula MX2 (M=Mo,W and X=S,Se), in bilayer and bulk MoS2, and in two MX2 hetero-bilayers. Our results elucidate the time scale and microscopic origin of light emission in TMDs, which have been the subjects of recent intense investigation. We find radiative lifetimes of a few ps at low temperature and a few ns at room temperature in the monolayers, and slower radiative recombination in bulk and bilayer than in monolayer MoS2. The MoS2/WS2 and MoSe2/WSe2 hetero-bilayers exhibit very long-lived (~30 ns at room temperature) inter-layer excitons constituted by electrons localized on the Mo-based and holes on the W-based monolayer; this finding agrees with very recent ultrafast spectroscopy experiments, and helps resolve a controversy on the topic. In closing, we discuss how the radiative lifetime tunability, together with the ability shown here to predict radiative lifetimes from computations, can be employed to manipulate excitons in TMDs and their heterostructures for application in optoelectronics and solar energy conversion.