The fatality rate of myocardial infarction ranks first in cardiovascular disease, which is myocardial necrosis caused by persistent ischemia and hypoxia caused by coronary artery occlusion. Myocardial infarction leads to the irreversible loss of a large number of cardiomyocytes. Exogenous cardiomyocyte supplement is an ideal method for the treatment of myocardial infarction. However, myocardial infarction leads to the loss of electrical conductivity of myocardial tissue at the infarcted site, and it is difficult for exogenous cardiomyocytes to integrate effectively. So, it is necessary to reshape the microenvironment of the infarcted site and restore its electrical conductivity. The construction of heart tissue engineering combined with biomaterials, cells and bioactive molecules is a hot topic in recent years. Conductive hydrogels, as an ideal scaffold material can promote the maturation of cardiomyocytes in vitro, give effective mechanical support to the infarcted site, improve the electrical conductivity of infarcted tissue, help exogenous cardiomyocytes integrate in vivo and restore heart function gradually. In this paper, we review the natural substrate materials used to make conductive hydrogels, the emerging trend of conductive materials and the applications of conductive hydrogels in heart tissue engineering.