The convergence of tissue engineering and patient-specific stem cell biology has enabled the engineering of in vitro tissue models that allow the study of patient-tailored treatment modalities. However, sex-related disparities in health and disease, from systemic hormonal influences to cellular-level differences, are often overlooked in stem cell biology, tissue engineering and preclinical screening. The cardiovascular system, in particular, shows considerable sex-related differences, which need to be considered in cardiac tissue engineering. In this Review, we analyse sex-related properties of the heart muscle in the context of health and disease, and discuss a framework for including sex-based differences in human cardiac tissue engineering. We highlight how sex-based features can be implemented at the cellular and tissue levels, and how sex-specific cardiac models could advance the study of cardiovascular diseases. Finally, we define design criteria for sex-specific cardiac tissue engineering and provide an outlook to future research possibilities beyond the cardiovascular system.