Quaternary carbon stereocentres-carbon atoms to which four distinct carbon substituents are attached-are common features of molecules found in nature. However, before recent advances in chemical catalysis, there were few methods of constructing single stereoisomers of this important structural motif. Here we discuss the many catalytic enantioselective reactions developed during the past decade for the synthesis of single stereoisomers of such organic molecules. This progress now makes it possible to incorporate quaternary stereocentres selectively in many organic molecules that are useful in medicine, agriculture and potentially other areas such as flavouring, fragrances and materials.