Oxidative stress plays a key role in carcinogenesis. Oxidative damage to cell components can lead to the initiation, promotion and progression of cancer. Oxidative stress is also a distinctive sign in several genetic disorders characterized by a cancer predisposition such as ataxia-telangiectasia, Fanconi anemia, Down syndrome, Beckwith-Wiedemann syndrome and Costello syndrome. Taking into account the link between oxidative stress and cancer, the capacity of antioxidant agents to prevent or delay neoplastic development has been tested in various studies, both in vitro and in vivo, with interesting and promising results. In recent years, research has been conducted into the molecular mechanisms linking oxidative stress to the pathogenesis of the genetic syndromes we consider in this review, with the resulting identification of possible new therapeutic targets. The aim of this review is to focus on the oxidative mechanisms intervening in carcinogenesis in cancer-prone genetic disorders and to analyze the current status and future prospects of antioxidants.