2D materials show wide-ranging physical properties with their electronic bandgaps varying from zero to several electronvolts, offering a rich platform to explore novel electronic and optoelectronic functions. Notably, atomically thin 2D materials are well suited for integration in optoelectronic circuits, because of their ultrathin body, strong light-matter interactions, and compatibility with the current silicon photonic technology. In this paper, an overview of the state of the art of using 2D materials in optoelectronic devices and integration is provided. The optoelectronic properties of 2D materials and their typical electronic and optoelectronic applications including light sources, optical modulators, photodetectors, field-effect transistors, and logic circuits are summarized. The device configurations, operation mechanisms, and device figures-of-merit are introduced and discussed. By discussing the recent advances, future trends, and existing challenges of 2D materials and their optoelectronic devices, this review has provided an insight into the perspectives of 2D materials for optoelectronic integration and may guide the development of this field within the research community.