Recent advances in the development of 2D-layered materials have witnessed the use of these materials as intriguing building blocks for various optoelectronic applications. The versatility of 2D material systems makes them particularly attractive for photodetection with fast response and high sensitivity over a broad spectral coverage, ranging from ultraviolet, visible to infrared. However, due to the atomically thin nature and inherent electronic structure, light that is harvested by monolayer 2D materials is extremely low and the photodetector devices often operate as Schottky junctions, which significantly limit the efficiency for photocurrent generation. Here, recent progress on the exploration of 2D material-based heterostructures and the engineering of the band structures for energy-efficient optoelectronic applications is reviewed. First, the strategies to introduce a bandgap in graphene are reviewed and discussed. This is followed by a discussion on the engineering of electronic structures in 2D transition metal dichalcogenides by localized chemical doping, dual gating, liquid gating, thickness modulation, and constructing heterojunctions. It is concluded by a summary and perspective on the challenges and future directions.