Our species has the peculiar ability to accumulate cultural innovations over multiple generations, a phenomenon termed `cumulative cultural evolution’ (CCE). Recent years have seen a proliferation of empirical and theoretical work exploring the interplay between demography and CCE. This has generated intense discussion about whether demographic models can help explain historical patterns of cultural changes. Here, we synthesize empirical and theoretical studies from multiple fields to highlight how both population size and structure can shape the pool of cultural information that individuals can build upon to innovate, present the potential pathways through which humans’ unique social structure might promote CCE, and discuss whether humans’ social networks might partly result from selection pressures linked to our extensive reliance on culturally accumulated knowledge.