Cardiovascular diseases remain the leading cause of human mortality worldwide. Some severe symptoms, including myocardial infarction and heart failure, are difficult to heal spontaneously or under systematic treatment due to the limited regenerative capacity of the native myocardium. Cardiac tissue engineering has emerged as a practical strategy to culture functional cardiac tissues and relieve the disorder in myocardium when implanted. In cardiac tissue engineering, the design of a scaffold is closely relevant to the function of the regenerated cardiac tissues. Nanofibrous materials fabricated by electrospinning have been developed as desirable scaffolds for tissue engineering applications because of the biomimicking structure of protein fibers in native extra cellular matrix. The versatilities of electrospinning on the polymer component, the fiber structure, and the functionalization with bioactive molecules have made the fabrication of nanofibrous scaffolds with suitable mechanical strength and biological properties for cardiac tissue engineering feasible. Here, an overview of recent advances in various electrospun scaffolds for engineering cardiac tissues, including the design of advanced electrospun scaffolds and the performance of the scaffolds in functional cardiac tissue regeneration, is provided with the aim to offer guidance in the innovation of novel electrospun scaffolds and methods for improving their potential for cardiac tissue engineering applications.