Individual differences in human intelligence, as assessed using cognitive test scores, have a well-replicated, hierarchical phenotypic covariance structure. They are substantially stable across the life course, and are predictive of educational, social, and health outcomes. From this solid phenotypic foundation and importance for life, comes an interest in the environmental, social, and genetic aetiologies of intelligence, and in the foundations of intelligence differences in brain structure and functioning. Here, we summarise and critique the last 10 years or so of molecular genetic (DNA-based) research on intelligence, including the discovery of genetic loci associated with intelligence, DNA-based heritability, and intelligence's genetic correlations with other traits. We summarise new brain imaging-intelligence findings, including whole-brain associations and grey and white matter associations. We summarise regional brain imaging associations with intelligence and interpret these with respect to theoretical accounts. We address research that combines genetics and brain imaging in studying intelligence differences. There are new, though modest, associations in all these areas, and mechanistic accounts are lacking. We attempt to identify growing points that might contribute toward a more integrated 'systems biology' account of some of the between-individual differences in intelligence.