Due to insufficient supply of heart transplants and limited regenerative ability of heart tissues, cardiac tissue engineering has emerged to restore or regenerate the structure and function of native cardiac tissues. Scaffolds play a major role in fabrication of functional cardiac tissues, providing structural support, biodegradation, and cell affinity. However, currently used scaffolds in cardiac tissue regeneration tend to lack adequate electrical conductivity and favorable mechanical properties. In response to these concerns, carbon nanotubes (CNTs) have been used to enhance electrical and mechanical properties of scaffolds in cardiac tissue engineering. Here, we review different hybrid CNT-biomaterial scaffolds, both natural and synthetic, in cardiac tissue regeneration and their fabrication methods. Furthermore, CNT toxicity is also discussed. We further outline future trends in this research area toward using CNTs as a functional nanomaterial in cardiac tissue engineering.