Cardiovascular diseases (CVDs) are the leading causes of mortality globally that demand the application of tissue engineering strategies to repair damaged tissues. Conventional tissue engineering approaches such as particulate leaching, hydrogels, gas foaming, solvent casting and electrospinning based strategies aim to develop extracellular matrix analogues to promote the regeneration of functional cardiac tissues. However, poor cell seeding efficiency with the non-uniform distribution of cells across thicker scaffolds (>5 mm) limits the clinical potential. The advent of 3D bioprinting offers layer-by-layer cellular integration and facilitates the recapitulation of cellular heterogeneity and intricate hierarchical structural organization. Although the success of 3D bioprinting of cardiac specific tissues has been demonstrated in varying degrees, maintaining unique architecture, cellular heterogeneity and cardiac functions demands the search for cardiac-specific bioinks. Hence, this review outlines the various bioinks explored in the printing of cardiac tissues and the essential properties such as rheological and electromechanical characteristics necessary for the functional restoration. This review further describes the application of 3D bioprinting for the fabrication of several cardiac tissues such as heart valves, coronary arteries, cardiac patches and whole heart. Finally, this review summarizes the existing limitations, unmet technical challenges and potential future focus on the expansion of bioprinting technique to cardiovascular medicine.