This is a concise statement of ten different problems for which a behavioural science should (and may soon be able to) provide coherent, empirically grounded explanations. These problems were chosen for their social importance as well as their theoretical interest, as demonstrations of the need to integrate psychological, economic and evolutionary factors in explanatory models. For each question, I mention pointers to incipent or possible research programmes. The questions are the following: What are the natural limits to family arrangements? Do we have an intuitive understanding of large societies? Why are despised social categories essentialised? Why gender differences in politics? What logic drives ethnic violence? How are moral concepts acquired? What drives people's economic intuitions? Are there cultural differences in low-level cognition? What explains individual religious attitudes? Why religious fundamentalism and extremism? The general aim is to propose a new approach to issues of human culture, not through an abstract discussion of paradigms and traditions, but through specific examples of possible empirical research.