In the past decade graphene has been one of the most studied material for several unique and excellent properties. Due to its two dimensional nature, physical and chemical properties and ease of manipulation, graphene offers the possibility of integration with the exiting semiconductor technology for next-generation electronic and sensing devices. In this context, the understanding of the graphene/semiconductor interface is of great importance since it can constitute a versatile standalone device as well as the building-block of more advanced electronic systems. Since graphene was brought to the attention of the scientific community in 2004, the device research has been focused on the more complex graphene transistors, while the graphene/semiconductor junction, despite its importance, has started to be the subject of systematic investigation only recently. As a result, a thorough understanding of the physics and the potentialities of this device is still missing. The studies of the past few years have demonstrated that graphene can form junctions with 3D or 2D semiconducting materials which have rectifying characteristics and behave as excellent Schottky diodes. The main novelty of these devices is the tunable Schottky barrier height, a feature which makes the graphene/semiconductor junction a great platform for the study of interface transport mechanisms as well as for applications in photo-detection, high-speed communications, solar cells, chemical and biological sensing, etc. In this paper, we review the state-of-the art of the research on graphene/semiconductor junctions, the attempts towards a modeling and the most promising applications.