(1) Receiving an oncological diagnosis involves countless physical and mental challenges for those who become ill. In addition to this, developmental activities are put on hold when a parent becomes ill, significantly impairing children's normal growth and development. The purpose of this review is to highlight the psychological impact of cancer on children, with particular attention to differences based on the age of the child and the stage of the parent's disease. (2) Articles published on PubMed up until October 2023 were searched. Qualitative and quantitative studies were included in this review after an evaluation of the full text. The study selection process was undertaken by two researchers, and articles for which there was unanimous agreement between researchers were included in the review. (3) Children's psycho-emotional responses differ based on their age and the disease stage. In general, good communication and a supportive family environment that understands everyone's needs seem to constitute important protective factors that favor the adaptation of the entire family to the disease. (4) The family, as an evolutionary system, finds itself facing phases typical of development. Knowing the variables that intervene in the process of adaptation to the disease will allow us to design specific and differentiated clinical interventions based on the needs of not only the patient but also the entire family.