Two-dimensional (2D) group-VI transition metal dichalcogenide (TMD) semiconductors, such as MoS₂, MoSe₂, WS₂ and others manifest strong light matter coupling and exhibit direct band gaps which lie in the visible and infrared spectral regimes. These properties make them potentially interesting candidates for applications in optics and optoelectronics. The excitons found in these materials are tightly bound and dominate the optical response, even at room temperatures. Large binding energies and unique exciton fine structure make these materials an ideal platform to study exciton behaviors in two-dimensional systems. This review article mainly focuses on studies of mechanisms that control dynamics of excitons in 2D systems – an area where there remains a lack of consensus in spite of extensive research. Firstly, we focus on the kinetics of dark and bright excitons based on a rate equation model and discuss on the role of previous ‘unsuspected’ dark excitons in controlling valley polarization. Intrinsically, dark and bright exciton energy splitting plays a key role in modulating the dynamics. In the second part, we review the excitation energy-dependent possible characteristic relaxation pathways of photoexcited carriers in monolayer and bilayer systems. In the third part, we review the extrinsic factors, in particular the defects that are so prevalent in single layer TMDs, affecting exciton dynamics, transport and non-radiative recombination such as exciton–exciton annihilation. Lastly, the optical response due to pump-induced changes in TMD monolayers have been reviewed using femtosecond pump–probe spectroscopy which facilitates the analysis of underlying physical process just after the excitation.