Speech is central to human life. However, how the human brain extracts meaning from the dynamic patterns of sound that constitute speech remains poorly understood. It is generally accepted that this ability is underpinned by hierarchical processing in the human brain, with much of the evidence in support of this idea having come from neuropsychology or brain imaging studies. However, both of these approaches have limitations with respect to studying the neurophysiological processing of many of the rapid, dynamic features of speech. In this talk I will discuss a series of studies aimed at using a model-based framework to analyse EEG responses to naturalistic speech stimuli. This will include describing our attempts to dissociate the general auditory processing of speech sounds from the linguistic processing of speech units and the process of language comprehension. It will also include consideration of how attention and multisensory input affect speech and language processing at different hierarchical levels. Finally, I will also discuss how we are using these approaches to study perceptual processing in patients with schizophrenia and people with autism.