This paper focuses on what electrical and magnetic recordings of human brain activity reveal about spoken language understanding. Based on the high temporal resolution of these recordings, a fine-grained temporal profile of different aspects of spoken language comprehension can be obtained. Crucial aspects of speech comprehension are lexical access, selection and semantic integration. Results show that for words spoken in context, there is no 'magic moment' when lexical selection ends and semantic integration begins. Irrespective of whether words have early or late recognition points, semantic integration processing is initiated before words can be identified on the basis of the acoustic information alone. Moreover, for one particular event-related brain potential (ERP) component (the N400), equivalent impact of sentence- and discourse-semantic contexts is observed. This indicates that in comprehension, a spoken word is immediately evaluated relative to the widest interpretive domain available. In addition, this happens very quickly. Findings are discussed that show that often an unfolding word can be mapped onto discourse-level representations well before the end of the word. Overall, the time course of the ERP effects is compatible with the view that the different information types (lexical, syntactic, phonological, pragmatic) are processed in parallel and influence the interpretation process incrementally, that is as soon as the relevant pieces of information are available. This is referred to as the immediacy principle.