Semantic impairments have been divided into storage deficits, in which the semantic representations themselves are damaged, and access deficits, in which the representations are intact but access to them is impaired. The behavioural phenomena that have been associated with access deficits include sensitivity to cueing, sensitivity to presentation rate, performance inconsistency, negative serial position effects, sensitivity to number and strength of competitors, semantic blocking effects, disordered selection between strong and weak competitors, correlation between semantic deficits and executive function deficits and reduced word frequency effects. Four general accounts have been proposed for different subsets of these phenomena: abnormal refractoriness, too much activation, impaired competitive selection and deficits of semantic control. A combination of abnormal refractoriness and impaired competitive selection can account for most ofthe behavioural phenomena, but there remain several open questions. In particular, it remains unclear whether access deficits represent a single syndrome, a syndrome with multiple subtypes or a variable collection of phenomena, whether the underlying deficit is domain-general or domain-specific, whether it is owing to disorders of inhibition, activation or selection, and the nature of the connection (if any) between access phenomena in aphasia and in neurologically intact controls. Computational models offer a promising approach to answering these questions. © 2013 The Author(s) Published by the Royal Society. All rights reserved.