"Weak central coherence" refers to the detail-focused processing style proposed to characterise autism spectrum disorders (ASD). The original suggestion of a core deficit in central processing resulting in failure to extract global form/meaning, has been challenged in three ways. First, it may represent an outcome of superiority in local processing. Second, it may be a processing bias, rather than deficit. Third, weak coherence may occur alongside, rather than explain, deficits in social cognition. A review of over 50 empirical studies of coherence suggests robust findings of local bias in ASD, with mixed findings regarding weak global processing. Local bias appears not to be a mere side-effect of executive dysfunction, and may be independent of theory of mind deficits. Possible computational and neural models are discussed.