Alexithymia is characterised by difficulty identifying and describing one’s own emotion. Identifying and describing one’s emotion involves several cognitive processes, so alexithymia may result from a number of impairments. Here we propose the alexithymia language hypothesis - the hypothesis that language impairment can give rise to alexithymia - and critically review relevant evidence from healthy populations, developmental disorders, adult-onset illness and acquired brain injury. We conclude that the available evidence is supportive of the alexithymia-language hypothesis, and therefore that language impairment may represent one of multiple routes to alexithymia. Where evidence is lacking, we outline which approaches will be useful in testing this hypothesis.