The advent of graphene and related 2D materials has recently led to a new technology: heterostructures based on these atomically thin crystals. The paradigm proved itself extremely versatile and led to rapid demonstration of tunnelling diodes with negative differential resistance, tunnelling transistors, photovoltaic devices and so on. Here, we take the complexity and functionality of such van der Waals heterostructures to the next level by introducing quantum wells (QWs) engineered with one atomic plane precision. We describe light-emitting diodes (LEDs) made by stacking metallic graphene, insulating hexagonal boron nitride and various semiconducting monolayers into complex but carefully designed sequences. Our first devices already exhibit an extrinsic quantum efficiency of nearly 10% and the emission can be tuned over a wide range of frequencies by appropriately choosing and combining 2D semiconductors (monolayers of transition metal dichalcogenides). By preparing the heterostructures on elastic and transparent substrates, we show that they can also provide the basis for flexible and semi-transparent electronics. The range of functionalities for the demonstrated heterostructures is expected to grow further on increasing the number of available 2D crystals and improving their electronic quality. ; This work was supported by The Royal Society, Royal Academy of Engineering, U.S. Army, European Science Foundation (ESF) under the EUROCORES Programme EuroGRAPHENE (GOSPEL), European Research Council, EC-FET European Graphene Flagship, Engineering and Physical Sciences Research Council (UK), the Leverhulme Trust (UK), U.S. Office of Naval Research, U.S. Defence Threat Reduction Agency, U.S. Air Force Office of Scientific Research, FP7 ITN S3 NANO, SEP-Mexico and CONACYT.