The diagnosis of schizophrenia rests on clinical criteria that cannot be assessed in animal models. Together with absence of a clear underlying pathology and understanding of what causes schizophrenia, this has hindered development of informative animal models. However, recent large-scale genomic studies have identified copy number variants (CNVs) that confer high risk of schizophrenia and have opened a new avenue for generation of relevant animal models. Eight recurrent CNVs have reproducibly been shown to increase the risk of schizophrenia by severalfold: 22q11.2(del), 15q13.3(del), 1q21(del), 1q21(dup), NRXN1(del), 3q29(del), 7q11.23(dup), and 16p11.2(dup). Five of these CNVs have been modeled in animals, mainly mice, but also rats, flies, and zebrafish, and have been shown to recapitulate behavioral and electrophysiological aspects of schizophrenia. Here, we provide an overview of the schizophrenia-related phenotypes found in animal models of schizophrenia high-risk CNVs. We also discuss strengths and limitations of the CNV models, and how they can advance our biological understanding of mechanisms that can lead to schizophrenia and can be used to develop new and better treatments for schizophrenia.