There is a tension between the conception of cognition as a central nervous system (CNS) process and a view of cognition as extending towards the body or the contiguous environment. The centralised conception requires large or complex nervous systems to cope with complex environments. Conversely, the extended conception involves the outsourcing of information processing to the body or environment, thus making fewer demands on the processing power of the CNS. The evolution of extended cognition should be particularly favoured among small, generalist predators such as spiders, and here, we review the literature to evaluate the fit of empirical data with these contrasting models of cognition. Spiders do not seem to be cognitively limited, displaying a large diversity of learning processes, from habituation to contextual learning, including a sense of numerosity. To tease apart the central from the extended cognition, we apply the mutual manipulability criterion, testing the existence of reciprocal causal links between the putative elements of the system. We conclude that the web threads and configurations are integral parts of the cognitive systems. The extension of cognition to the web helps to explain some puzzling features of spider behaviour and seems to promote evolvability within the group, enhancing innovation through cognitive connectivity to variable habitat features. Graded changes in relative brain size could also be explained by outsourcing information processing to environmental features. More generally, niche-constructed structures emerge as prime candidates for extending animal cognition, generating the selective pressures that help to shape the evolving cognitive system.