How has human culture become so complex? We argue that a key process is social tinkering: the gradual accumulation of ad hoc innovations to the social rules that coordinate behavior in response to immediate challenges. Momentary innovations provide precedents that can be reused, entrenched, adapted and recombined to handle future challenges. Interactions between these social rules create rich cultural systems (languages, ethics, political organization) of increasing complexity through processes of spontaneous order, not deliberate design. To explain the historical emergence of cumulative cultural complexity, we distinguish between six overlapping and interacting stages: (1) non-social tinkering to solve problems in the natural world; (2) learning and copying from the tinkering of others; (3) social tinkering involving jointly agreeing on momentary conventions to coordinate interactions, typically for mutual benefit; (4) creating communicative conventions (language) to support more complex social interactions; (5) social tinkering of linguistically-formulated cultural rules leading to laws, organizations, institutions, etc.; and (6) tinkering with linguistically-formulated non-social knowledge, allowing for the creation of science and technology. The rich interplay of innovation across the six stages is crucial for explaining increasing cultural and organizational complexity and our collective mastery of the natural world. Because social and non-social tinkering requires two different kinds of learning, this analysis has important implications for the understanding of human learning and cognition, including moral and evolutionary psychology, theory of mind, and the view of the child-as-scientist. Social tinkering also has substantial implications for current theories of cultural evolution.