The goal of this article is to make the case for a radical exemplar account of child language acquisition, under which unwitnessed forms are produced and comprehended by on-the-fly analogy across multiple stored exemplars, weighted by their degree of similarity to the target with regard to the task at hand. Across the domains of (1) word meanings, (2) morphologically inflected words, (3) "n"-grams, (4) sentence-level constructions and (5) phonetics and phonology, accounts based on independently-represented abstractions (whether formal rules or prototype categories) fail for two reasons. First, it is not possible to posit abstractions that delineate possible and impossible form; e.g. that (1) rule in pool "tables" and data "tables," but rule out chairs, (2) rule in the past-tense forms "netted" and "bet" but rule out *"setted" and *"jet," (3) rule in the bigram "f+t" but rule out (probabilistically) "v+t," (4) rule in both "John feared Bill" and "John frightened Bill" but rule out *"John laughed Bill," (5) rule in Speaker A but rule out Speaker B as the person who produced a particular word (e.g. "Sa'urday"). Second, for each domain, empirical data provide evidence of exemplar storage that cannot be captured by putative abstractions: e.g. speakers prefer and/or show an advantage for (1) exemplar variation even within word-meaning 'category boundaries', (2) novel inflected forms that are similar to existing exemplars, (3) n-grams that have occurred frequently in the input, (4) SVO sentences with "he" as SUBJECT and "it" as OBJECT and (5) repeated productions of 'the same' word that are phonologically similar or, better still, identical. An exemplar account avoids an intractable lumping-or-splitting dilemma facing abstraction-based accounts and provides a unitary explanation of language acquisition across all domains; one that is consistent with models and empirical findings from the computational modelling and neuroimaging literature.