Implantable cardiac patches and injectable hydrogels are among the most promising therapies for cardiac tissue regeneration following myocardial infarction. Incorporating electrical conductivity into these patches and hydrogels is found to be an efficient method to improve cardiac tissue function. Conductive nanomaterials such as carbon nanotube, graphene oxide, gold nanorod, as well as conductive polymers such as polyaniline, polypyrrole, and poly(3,4-ethylenedioxythiophene):polystyrene sulfonate are appealing because they possess the electroconductive properties of semiconductors with ease of processing and have potential to restore electrical signaling propagation through the infarct area. Numerous studies have utilized these materials for regeneration of biological tissues that possess electrical activities, such as cardiac tissue. In this review, recent studies on the use of electroconductive materials for cardiac tissue engineering and their fabrication methods are summarized. Moreover, recent advances in developing electroconductive materials for delivering therapeutic agents as one of emerging approaches for treating heart diseases and regenerating damaged cardiac tissues are highlighted.