Despite the fact that much is known about the taxonomy and predictive validity of human intelligence differences, there has been relatively little progress in understanding their cognitive bases. However, some recent firm findings mark the beginnings of a cognitive reductionism in human intelligence. Progress towards discovering 'cognitive components' that, firstly, show individual differences and, secondly, relate to psychometric intelligence differences is described here at different nominal levels of analysis: 'psychometric', 'cognitive-experimental' and 'psychophysical'. The field of intelligence differences remains a fertile yet seriously under-developed demesne in which cognitive scientists should collaborate with differential psychologists.