Human social life is uniquely complex and diverse. Much of that complexity consists of culturally transmitted ideas and skills that underpin the operation of institutions that structure our social life. Considerable theoretical and empirical work has been devoted to the role of cultural evolutionary processes in the evolution of institutions. The most persistent controversy has been over the role of cultural group selection and gene-culture coevolution in early human populations the Pleistocene. We argue that cultural group selection and related cultural evolutionary processes had an important role in shaping the innate components of our social psychology. By the Upper Paleolithic humans seem to have lived in societies structured by institutions, as do modern populations living in simple societies. The most ambitious attempts to test these ideas have been the use of experimental games in field settings to document human similarities and differences on theoretically interesting dimensions. These studies have documented a huge range of behavior cross-culturally, although no societies so far examined follow the expectations of selfish rationality. These data are at least consistent with operation of cultural group selection and gene-culture coevolution operating in the deep tribal past and with the contemporary importance of cultural evolution in the evolution of institutions and institutional diversity.