Cardiovascular diseases, the major international health problem and the leading cause of death worldwide have been increasing in recent years due to population aging and lifestyle changes. Loss of cardiac muscle function after myocardial damage is one of the most critical challenges in cardiovascular medicine that has not yet been overcome. Tissue engineering (TE) has emerged as a promising therapeutic approach in modern medicine, targeting the substitution of damaged tissue with functional tissue grown inside an artificial scaffold. Great efforts have been made toward the construction of tissue engineering scaffolds that paved the way for extracellular matrix (ECM)-like biomaterial. In cardiac tissue engineering, key parameters must be determined to select the ideal biomaterial, such as biocompatibility, conductivity, mechanical features, degradation and swelling rate, surface properties, and cell viability, growth and proliferation. Among different scaffolding materials, a wide range of natural biological macromolecules and synthetic macromolecules have been utilized to produce scaffolds with multifunctionality for cardiac tissue engineering (CTE). In this review, we have focused on recent achievements in the field of synthetic biodegradable macromolecules (such as aliphatic polyesters, polyurethane, poly (glycerol sebacate)) and the significant strategies to construct electrically conductive scaffolds to regenerate the function of native cardiac tissue. These biodegradable macromolecules have several attractive properties, including biocompatibility, elasticity, good mechanical properties, compatibility with native cardiac tissue, and proper surface biochemistry to increase cardiac cell adhesion, making them appropriate candidates for CTE. Recently, a growing trend in the use of conductive scaffolds for cardiac regeneration has been witnessed. Different materials ranging from metals, ceramics, and polymers have been used as parts of conductive scaffolds for CTE, possessing conductivity assortments from a range of semiconductive to conductive. Moreover, this review paper also focuses on the main strategies to create electroconductive scaffolds for in vitro cardiac muscle regeneration.