Recent progress on the synthesis and characterization of semiconductor nanowire heterostructures is reviewed. We describe a general method for heterostructure synthesis based on chemical vapour deposition and the vapour-liquid-solid growth of crystalline semiconducting nanowires. We then examine examples of nanowire heterostructures for which physical properties have been measured, considering the effects of synthetic conditions on the heterointerfaces as well as the electrical and optical characterization measurements that reveal heterointerface formation and quality. Finally, we identify areas of technical and conceptual progress that can contribute to the development of functional nanowire heterostructures.