Recent research in two-dimensional (2D) materials has boosted a renovated interest in the p-n junction, one of the oldest electrical components which can be used in electronics and optoelectronics. 2D materials offer remarkable flexibility to design novel p-n junction device architectures, not possible with conventional bulk semiconductors. In this Review we thoroughly describe the different 2D p-n junction geometries studied so far, focusing on vertical (out-of-plane) and lateral (in-plane) 2D junctions and on mixed-dimensional junctions. We discuss the assembly methods developed to fabricate 2D p-n junctions making a distinction between top-down and bottom-up approaches. We also revise the literature studying the different applications of these atomically thin p-n junctions in electronic and optoelectronic devices. We discuss experiments on 2D p-n junctions used as current rectifiers, photodetectors, solar cells and light emitting devices. The important electronics and optoelectronics parameters of the discussed devices are listed in a table to facilitate their comparison. We conclude the Review with a critical discussion about the future outlook and challenges of this incipient research field.