Culture is increasingly being framed as a driver of human phenotypes and behaviour. Yet very little is known about variations in the patterns of past social interactions between humans in cultural evolution. The archaeological record, combined with modern evolutionary and analytical approaches, provides a unique opportunity to investigate broad-scale patterns of cultural change. Prompted by evidence that a population's social connectivity influences cultural variability, in this article, we revisit traditional approaches used to infer cultural evolutionary processes from the archaeological data. We then propose that frameworks considering multi-scalar interactions (from individuals to populations) over time and space have the potential to advance knowledge in cultural evolutionary theory. We describe how social network analysis can be applied to analyse diachronic structural changes and test cultural transmission hypotheses using the archaeological record (here specifically from the Marine Isotope Stage 3 ca 57–29 ka onwards). We argue that the reconstruction of prehistoric networks offers a timely opportunity to test the interplay between social connectivity and culture and ultimately helps to disentangle evolutionary mechanisms in the archaeological record. This article is part of a discussion meeting issue ‘The emergence of collective knowledge and cumulative culture in animals, humans and machines’. This work was funded by the European Research Council (ref. ERC-CoG 2015) under the European Union's horizon 2020 research and innovation programme (grant agreement no. 683018). J.F.-L.d.P. was also supported by grant no. 2018/040 from the CIDEGENT Excellence programme of Generalitat Valenciana.