Hemispheric specialization for language is one of the most robust findings of cognitive neuroscience. In this review, we first present the main hypotheses about the origins of this important aspect of brain organization. These theories are based in part on the main approaches to hemispheric specialization: studies of aphasia, anatomical asymmetries and, nowadays, neuroimaging. All these approaches uncovered a large inter-individual variability which became the bulk of research on hemispheric specialization. This is why, in a second part of the review, we present the main facts about inter-individual variability, trying to relate findings to the theories presented in the first part. This review focuses on neuroimaging as it has recently given important results, thanks to investigations of both anatomical and functional asymmetries in healthy subjects. Such investigations have confirmed that left-handers, especially "familial left-handers", are more likely to have an atypical pattern of hemispheric specialization for language. Differences between men and women seem less evident although a less marked hemispheric specialization for language was depicted in women. As for the supposed relationship between anatomical and functional asymmetries, it has been shown that the size of the left (not the right) planum temporale could explain part of the variability of left hemispheric specialization for language comprehension. Taken as a whole, findings seem to vary with language tasks and brain regions, therefore showing that hemispheric specialization for language is multi-dimensional. This is not accounted for in the existing models of hemispheric specialization.