Cardiovascular diseases pose a significant global health challenge, driving ongoing efforts to develop effective treatments. Various biofabrication technologies utilizing numerous materials have been employed to design functional cardiac tissues. Choosing the right material is crucial to support cardiac cell growth, proliferation, tissue maturation and functionality. 3D printing enables the fabrication of structures that mimic the hierarchical organization of native cardiac tissue, further enhancing its function. Electrospinning produces nanofibrous scaffolds with a high surface area and porosity, mimicking the extracellular matrix and promoting the cell behaviors required for tissue formation. Although typically employed independently, combining these technologies can enable the fabrication of patches with properties closely resembling those of native cardiac tissues. Recent research focuses on the use of electroconductive materials, which enhance cell-to-cell communication and promote the maturation of cardiomyocytes, thereby preventing arrhythmic contractions and improving the functionality of engineered cardiac tissues. In this review, recent studies showcasing the applications of electroconductive biopolymer-based fibrous materials and hydrogels designed using 3D printing and/or electrospinning for cardiac tissue engineering are discussed. Furthermore, the review evaluates the synergistic effects of biopolymer-based materials and electrical components in 3D printed electroconductive hydrogels. It also discusses the challenges faced in fabricating these hydrogels and explores their future prospects for biomedical applications.