As a two-dimensional (2D) material, molybdenum disulfide (MoS2) exhibits unique electronic and optical properties useful for a variety of optoelectronic applications including light harvesting. In this article, we review recent progress in the synthesis, properties and applications of MoS2 and related heterostructures. Heterostructured materials are developed to add more functionality or flexibility compared to single component materials. Our focus is on their novel properties and functionalities as well as emerging applications, especially in the areas of light energy harvesting or conversion. We highlight the correlation between structural properties and other properties including electronic, optical, and dynamic. Whenever appropriate, we also try to provide fundamental insight gained from experimental as well as theoretical studies. Finally, we discuss some current challenges and opportunities in technological applications of MoS2.