The 'rapid temporal processing' and the 'temporal sampling framework' hypotheses have been proposed to account for the deficits in language and literacy development seen in specific language impairment and dyslexia. This paper reviews these hypotheses and concludes that the proposed causal chains between the presumed auditory processing deficits and the observed behavioural manifestation of the disorders are vague and not well established empirically. Several problems and limitations are identified. Most data concern correlations between distantly related tasks, and there is considerable heterogeneity and variability in performance as well as concerns about reliability and validity. Little attention is paid to the distinction between ostensibly perceptual and metalinguistic tasks or between implicit and explicit modes of performance, yet measures are assumed to be pure indicators of underlying processes or representations. The possibility that diagnostic categories do not refer to causally and behaviourally homogeneous groups needs to be taken seriously, taking into account genetic and neurodevelopmental studies to construct multiple-risk models. To make progress in the field, cognitive models of each task must be specified, including performance domains that are predicted to be deficient versus intact, testing multiple indicators of latent constructs and demonstrating construct reliability and validity.