Idioms are strings of words whose figurative meaning does not necessarily derive from that of the constituent parts. They belong to the vast and heterogeneous realm of multiword expressions, i.e. literal and non-literal word clusters whose representations are stored in semantic memory. This article provides an updated review of the psycholinguistic and electrophysiological literature on the processes underlying idiom comprehension with specific reference to the cues that lead to idiom recognition, to the syntactic and semantic behavior of idioms, to the relationships between literal compositionality and idiomatic meaning retrieval. Behavioral models of idiom comprehension are presented and discussed also with respect to the electrophysiological correlates of idiom and figurative language comprehension.