Osmotic power generation, the extraction of power from mixing salt solutions of different concentrations, can provide an efficient power source for both nanoscale and industrial-level applications. Power is generated using ion-selective channels or pores of nanometric dimensions in synthetic membrane materials. 2D materials such as graphene and MoS2 provide energy extraction efficiencies that are several orders of magnitude higher than those of more established bulky membranes. In this Review, we survey the current state of the art in power generation with both 2D materials and solid-state devices. We discuss the current understanding of the processes underlying power generation in boron nitride nanotubes and 2D materials, as well as the available fabrication methods and their impact on power generation. Finally, we overview future directions of research, which include increasing efficiency, upscaling single pores to porous membranes and solving other issues related to the potential practical application of 2D materials for osmotic power generation.