Human demographic and ecological success is frequently attributed to our capacity for cumulative culture, which allows human knowledge and technology to build up and improve over time. Yet it remains a mystery why other animals might possess socially learned traditions but lack this capacity for cumulative cultural knowledge gain. Nor is it immediately apparent what cognitive, social or demographic factors are necessary for accumulation to occur. Here I explore the factors that led to the evolution of the human cultural capability, drawing on a combination of experimental and theoretical approaches. I will present insights from the social learning strategies tournament, and comparative statistical analyses of primate social learning, which together imply that there may have been selection for increasing reliance on social learning, and for increasingly efficient (including higher fidelity) forms of copying, in the primate lineage leading to humans. I will go on to describe mathematical cultural evolution models that suggest that higher fidelity cultural transmission increases the longevity and amount of cultural traits, and that this in turn promotes cumulative cultural learning. I will move on to describe a mathematical model of the evolution of teaching, which is a mechanism for high-fidelity information transmission, which finds that teaching is more likely to evolve in a cumulative, compared to a non-cumulative, cultural learning context, implying that teaching and cumulative culture may have coevolved. Finally, I will present the findings of an experimental study of cumulative cultural learning involving human children, chimpanzees and capuchin monkeys, which implicates specific cognitive factors as central to cumulative learning, including imitation, teaching, language and prosocial behaviour. Presented by Kevin Laland (Biology, University of St Andrews, UK). Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/