Despite the clear divisions in current archaeological theories, in the last 30 years a ‘new consensus’ is emerging; this is the recognition that materials can actively shape human behaviour and cognition. While this recognition offers major opportunities for explaining changes in the archaeological record without just succumbing to individual simplistic models – such as migration or diffusion, or acculturation or convergence – there is still a need to formulate a framework that allows schematising this new consensus into our classifications and analyses of archaeological materials. Our paper aims to take a first step in this direction by formalising some mechanisms through which human behaviour and cognition can be modified by the material world. Operating at the interstices between theories about material engagement, cognition, and practice, three mechanisms of transformation are formalised, i.e., visual enchantment, mechanical degradation and obtrusion. As a further step to integrate these mechanisms, we stress the need to factor in human expectations, the changing states of materials and contingent situations into our schematisations and reconstructions of human–material relations.