Cardiovascular disease is the leading cause of death worldwide and the most common cause is myocardial infarction. Therefore, appropriate approaches should be used to repair damaged heart tissue. Recently, cardiac tissue engineering approaches have been extensively studied. Since the creation of the nature of cardiovascular tissue engineering, many advances have been made in cellular and scaffolding technologies. Due to the hydrated and porous structures of the hydrogel, they are used as a support matrix to deliver cells to the infarct tissue. In heart tissue regeneration, bioactive and biodegradable hydrogels are required by simulating native tissue microenvironments to support myocardial wall stress in addition to preserving cells. Recently, the use of nanostructured hydrogels has increased the use of nanocomposite hydrogels and has revolutionized the field of cardiac tissue engineering. Therefore, to overcome the limitation of the use of hydrogels due to their mechanical fragility, various nanoparticles of polymers, metal, and carbon are used in tissue engineering and create a new opportunity to provide hydrogels with excellent properties. Here, the types of synthetic and natural polymer hydrogels, nanocarbon-based hydrogels, and other nanoparticle-based materials used for cardiac tissue engineering with emphasis on conductive nanostructured hydrogels are briefly introduced.