It is recognized that developing valid animal models is essential for the research on the neurobiological mechanisms of (and treatments for) psychiatric disorders, even when these are as complex as schizophrenia. To be considered a valid analogue of the disorder, a given model should present good face validity (i.e. similarity of symptoms), good predictive validity (i.e. similarity of treatment effects and potential for discovering novel treatments) and enough construct validity (i.e. the model should help discover neurobiological mechanisms underlying the disorder or some relevant symptoms). The complexity of symptoms (positive, negative and cognitive) of schizophrenia makes it a very difficult task for a model to mimic all the main features of the disorder, but some rodent (mouse and rat) models have behavioural and even neurobiological phenotype characteristics resembling positive-like symptoms, cognitive symptoms and some neurochemical features of schizophrenia. As several recent works have already reviewed the main behavioural and developmental models, as well as the most used drug-induced, lesion-induced and genetic mouse models, the present review focuses on describing the most relevant genetically-based rat models of schizophrenia-relevant symptoms. Thus, we discuss several selective breeding programs leading to rat lines/strains which present impaired prepulse inhibition (PPI) of the acoustic startle response and (in some cases) latent inhibition deficits (both of which may be considered as endophenotypes of schizophrenia related with pre-attentive processes and attention, respectively), as well as other schizophrenia-relevant symptoms (e.g. learning deficits). Evidence is presented for the effects of genetic background on PPI (and other symptoms/phenotypes), as well as for environmental influences on genetic predisposition to enhanced apomorphine (mixed dopamine receptor agonist) effects. Some of the described rat models appear to present face validity and, to a certain extent, construct validity. While efforts should be made to evaluate the predictive validity of these genetic rat models, we propose that they have the advantage (over mouse knockouts, for example) of better representing “normal” genetic, neurobiological and phenotype variation, thus allowing the study of associations among them by means of genetic mapping or gene expression studies.