The p-n diodes represent the most fundamental device building block for diverse optoelectronic functions, but are difficult to achieve in atomically thin transition metal dichalcogenides (TMDs) due to the inability to selectively dope them into p- or n-type semiconductors. Here we report the first demonstration of an atomically thin and atomically sharp heterojunction p-n diode by vertically stacking p-type monolayer tungsten diselenide (WSe2) and n-type few-layer molybdenum disulfide (MoS2). Electrical measurement demonstrates excellent diode characteristics with well-defined current rectification behaviour and an ideality factor of 1.2. Photocurrent mapping shows fast photoresponse over the entire overlapping region with a highest external quantum efficiency up to 12 %. Electroluminescence studies show prominent band edge excitonic emission and strikingly enhanced hot electron luminescence. A systematic investigation shows distinct layer-number dependent emission characteristics and reveals important insight about the origin of hot-electron luminescence and the nature of electron-orbital interaction in TMDs. We believe that these atomically thin heterojunction p-n diodes represent an interesting system for probing the fundamental electro-optical properties in TMDs, and can open up a new pathway to novel optoelectronic devices such as atomically thin photodetectors, photovoltaics, as well as spin-/valley-polarized light emitting diodes and on-chip lasers. ; Comment: 27 pages, 7 figures