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This work reviews a number of existing computational studies concentrated on the question of how spoken language can be learned from continuous speech in the absence of linguistically or phonetically motivated background knowledge, a situation faced by human infants when they first attempt to learn their native language. Specifically, the focus is on how phonetic categories and word-like units can be acquired purely on the basis of the statistical structure of speech signals, possibly aided by some articulatory or visual constraints. The outcomes and shortcomings of the existing work are reflected onto findings from experimental and theoretical studies. Finally, some of the open questions and possible future research directions related to the computational models of language acquisition are discussed.