Birth defects contribute to ∼0.3% of global infant mortality in the first month of life, and congenital heart disease (CHD) is the most common birth defect among newborns worldwide. Despite the significant impact on human health, most treatments available for this heterogenous group of disorders are palliative at best. For this reason, the complex process of cardiogenesis, governed by multiple interlinked and dose-dependent pathways, is well investigated. Tissue, animal and, more recently, computerized models of the developing heart have facilitated important discoveries that are helping us to understand the genetic, epigenetic and mechanobiological contributors to CHD aetiology. In this Review, we discuss the strengths and limitations of different models of normal and abnormal cardiogenesis, ranging from single-cell systems and 3D cardiac organoids, to small and large animals and organ-level computational models. These investigative tools have revealed a diversity of pathogenic mechanisms that contribute to CHD, including genetic pathways, epigenetic regulators and shear wall stresses, paving the way for new strategies for screening and non-surgical treatment of CHD. As we discuss in this Review, one of the most-valuable advances in recent years has been the creation of highly personalized platforms with which to study individual diseases in clinically relevant settings.