This survey presents the most relevant neural network models of autism spectrum disorder and schizophrenia, from the first connectionist models to recent deep network architectures. We analyzed and compared the most representative symptoms with its neural model counterpart, detailing the alteration introduced in the network that generates each of the symptoms, and identifying their strengths and weaknesses. We additionally cross-compared Bayesian and free-energy approaches, as they are widely applied to modeling psychiatric disorders and share basic mechanisms with neural networks. Models of schizophrenia mainly focused on hallucinations and delusional thoughts using neural dysconnections or inhibitory imbalance as the predominating alteration. Models of autism rather focused on perceptual difficulties, mainly excessive attention to environment details, implemented as excessive inhibitory connections or increased sensory precision. We found an excessive tight view of the psychopathologies around one specific and simplified effect, usually constrained to the technical idiosyncrasy of the used network architecture. Recent theories and evidence on sensorimotor integration and body perception combined with modern neural network architectures could offer a broader and novel spectrum to approach these psychopathologies. This review emphasizes the power of artificial neural networks for modeling some symptoms of neurological disorders but also calls for further developing these techniques in the field of computational psychiatry.