Emerging trends for cardiac tissue engineering are focused on increasing the biocompatibility and tissue regeneration ability of artificial heart tissue by incorporating various cell sources and bioactive molecules. Although primary cardiomyocytes can be successfully implanted, clinical applications are restricted due to their low survival rates and poor proliferation. To develop successful cardiovascular tissue regeneration systems, new technologies must be introduced to improve myocardial regeneration. Electrospinning is a simple, versatile technique for fabricating nanofibers. Here, we discuss various biodegradable polymers (natural, synthetic, and combinatorial polymers) that can be used for fiber fabrication. We also describe a series of fiber modification methods that can increase cell survival, proliferation, and migration and provide supporting mechanical properties by mimicking micro-environment structures, such as the extracellular matrix (ECM). In addition, the applications and types of nanofiber-based scaffolds for myocardial regeneration are described. Finally, fusion research methods combined with stem cells and scaffolds to improve biocompatibility are discussed.