Two-dimensional (2D) semiconductors such as transition metal dichalcogenides (TMDCs) and black phosphorous have drawn tremendous attention as an emerging optical material due to their unique and remarkable optical properties. In addition, the ability to create the atomically-controlled van der Waals (vdW) heterostructures enables realizing novel optoelectronic devices that are distinct from conventional bulk counterparts. In this short review, we first present the atomic and electronic structures of 2D semiconducting TMDCs and their exceptional optical properties, and further discuss the fabrication and distinctive features of vdW heterostructures assembled from different kinds of 2D materials with various physical properties. We then focus on reviewing the recent progress on the fabrication of 2D semiconductor optoelectronic devices based on vdW heterostructures including photodetectors, solar cells, and light-emitting devices. Finally, we highlight the perspectives and challenges of optoelectronics based on 2D semiconductor heterostructures.