Computational modeling has well-established utility in the study of cardiovascular hemodynamics, with applications in medical research and, increasingly, in clinical settings to improve the diagnosis and treatment of cardiovascular diseases. Most cardiovascular models developed to date have been of the adult circulatory system; however, the perinatal period is unique as cardiovascular physiology undergoes drastic changes from the fetal circulation, during the birth transition, and into neonatal life. There may also be further complications in this period: for example, preterm birth (defined as birth before 37 completed weeks of gestation) carries risks of short-term cardiovascular instability and is associated with increased lifetime cardiovascular risk. Here, we review computational models of the cardiovascular system in early life, their applications to date and potential improvements and enhancements of these models. We propose a roadmap for developing an open-source cardiovascular model that spans the fetal, perinatal, and postnatal periods. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Congenital Diseases > Computational Models.