Ecological neutral theory refers to a suite of neutral models that all assume the demographic properties of an individual are independent of its species identity. This is a strong assumption that precludes explicit ecological niches or trophic interactions. Nevertheless, neutral models have been historically successful in replicating classic ecological patterns and linking these to mechanisms in insightful ways. Here we review the species–area relationship (SAR) predicted by various neutral models in different contexts. We discuss ‘mainland SARs’ relevant to large swathes of uninterrupted habitat and show that neutral theory predicts a triphasic SAR shape across broad spatial scales. We discuss ‘island SARs’ relevant to isolated patches of habitat and show that neutral theory predicts no effect of area and a single species for small islands and potentially rich behaviour for larger islands which may harbour endemic species. We also discuss two more complex types of SAR corresponding to cases where the areas sampled and sometimes the habitat itself are distributed unevenly across space in a fragmented pattern. We conclude by demonstrating specific applications of neutral SARs, including calculating extinction debt as well as optimal design of sampling schemes and nature reserves.