Individual differences in intelligence (cognitive abilities) are a prominent aspect of human psychology, and play a substantial role in influencing important life outcomes. Their phenotypic structure-as described by the science of psychometrics-is well understood and well replicated. Approximately half of the variance in a broad range of cognitive abilities is accounted by a general cognitive factor (g), small proportions of cognitive variance are caused by separable broad domains of mental function, and the substantial remainder is caused by variance that is unique to highly specific cognitive skills. The heritability of g is substantial. It increases from a low value in early childhood of about 30%, to well over 50% in adulthood, which continues into old age. Despite this, there is still almost no replicated evidence concerning the individual genes, which have variants that contribute to intelligence differences. Here, we describe the human intelligence phenotype, summarise the evidence for its heritability, provide an overview of and comment on molecular genetic studies, and comment on future progress in the field.