Cardiovascular diseases are a leading cause of death worldwide. Current treatments directed at heart repair have several disadvantages, such as a lack of donors for heart transplantation or non-bioactive inert materials for replacing damaged tissue. Because of the natural lack of regeneration of cardiomyocytes, new treatment strategies involve stimulating heart tissue regeneration. The basic three elements of cardiac tissue engineering (cells, growth factors, and scaffolds) are described in this review, with a highlight on the role of artificial scaffolds. Scaffolds for cardiac tissue engineering are tridimensional porous structures that imitate the extracellular heart matrix, with the ability to promote cell adhesion, migration, differentiation, and proliferation. In the heart, there is an important requirement to provide scaffold cellular attachment, but scaffolds also need to permit mechanical contractility and electrical conductivity. For researchers working in cardiac tissue engineering, there is an important need to choose an adequate artificial scaffold biofabrication technique, as well as the ideal biocompatible biodegradable biomaterial for scaffold construction. Finally, there are many suitable options for researchers to obtain scaffolds that promote cell–electrical interactions and tissue repair, reaching the goal of cardiac tissue engineering.