Human pluripotent stem cells (hPSCs) have extensive applications in fundamental biology, regenerative medicine, disease modelling, and drug discovery/toxicology. Whilst large numbers of cardiomyocytes can be generated from hPSCs, extensive characterization has revealed that they have immature cardiac properties. This has raised potential concerns over their usefulness for many applications and has led to the pursuit of driving maturation of hPSC-cardiomyocytes. Currently, the best approach for driving maturity is the use of tissue engineering to generate highly functional three-dimensional heart tissue. Although we have made significant progress in this area, we have still not generated heart tissue that fully recapitulates all the properties of an adult heart. Deciphering the processes driving cardiomyocyte maturation will be instrumental in uncovering the mechanisms that govern optimal heart function and identifying new therapeutic targets for heart disease.