People with synaesthesia have additional perceptual experiences, which are automatically and consistently triggered by specific inducing stimuli. Synaesthesia therefore offers a unique window into the neurocognitive mechanisms underlying conscious perception. A long-standing question in synaesthesia research is whether it is possible to artificially induce non-synaesthetic individuals to have synaesthesia-like experiences. Although synaesthesia is widely considered a congenital condition, increasing evidence points to the potential of a variety of approaches to induce synaesthesia-like experiences, even in adulthood. Here, we summarize a range of methods for artificially inducing synaesthesia-like experiences, comparing the resulting experiences to the key hallmarks of natural synaesthesia which include consistency, automaticity and a lack of 'perceptual presence'. We conclude that a number of aspects of synaesthesia can be artificially induced in non-synaesthetes. These data suggest the involvement of developmental and/or learning components in the acquisition of synaesthesia, and they extend previous reports of perceptual plasticity leading to dramatic changes in perceptual phenomenology in adults. This article is part of a discussion meeting issue 'Bridging senses: novel insights from synaesthesia'.