We review the hypotheses concerning the association between the paternal age at childbearing and childhood psychiatric disorders (autism spectrum- and attention deficit/hyperactive disorder) and adult disorders (schizophrenia, bipolar-, obsessive-compulsive-, and major depressive disorder) based on epidemiological studies. Several hypotheses have been proposed to explain the paternal age effect. We discuss the four main-not mutually exclusive-hypotheses. These are the de novo mutation hypothesis, the hypothesis concerning epigenetic alterations, the selection into late fatherhood hypothesis, and the environmental resource hypothesis. Advanced paternal age in relation to autism spectrum disorders and schizophrenia provided the most robust epidemiological evidence for an association, with some studies reporting a monotonic risk increase over age, and others reporting a marked increase at a given age threshold. Although there is evidence for the de novo mutation hypothesis and the selection into late fatherhood hypothesis, the mechanism(s) underlying the association between advanced paternal age and psychiatric illness in offspring remains to be further clarified.