In the classical twin design, researchers compare trait resemblance in cohorts of identical and non-identical twins to understand how genetic and environmental factors correlate with resemblance in behaviour and other phenotypes. The twin design is also a valuable tool for studying causality, intergenerational transmission, and gene–environment correlation and interaction. Here we review recent developments in twin studies, recent results from twin studies of new phenotypes and recent insights into twinning. We ask whether the results of existing twin studies are representative of the general population and of global diversity, and we conclude that stronger efforts to increase representativeness are needed. We provide an updated overview of twin concordance and discordance for major diseases and mental disorders, which conveys a crucial message: genetic influences are not as deterministic as many believe. This has important implications for public understanding of genetic risk prediction tools, as the accuracy of genetic predictions can never exceed identical twin concordance rates. The authors summarize the most recent developments in twin studies, recent results from twin studies of new phenotypes and new insights into twinning as a phenotype. They also provide an updated overview of twin concordance and discordance for major diseases and mental disorders.