Over the past decade a number of Graphene Based Materials (GBM) have been reported as electrodes for electrocardiogram (ECG) sensing. A wide variety of GBM electrodes have become available, enabling novel electrodes with several degrees of freedom, such as flexibility, strechability, and washability to potentially outperform conventional Silver/Silver Chloride (Ag/AgCl) electrodes. This paper provides a critical analysis of the recent advances in GBM electrodes for monitoring ECG signals. The results show that heart monitoring is possible with GBM electrodes, at the cost of a generally reduced Signal-to-Noise Ratio compared to conventional Ag/AgCl electrodes. The benefit is that the potential for flexible electrodes, and electrodes integrated into textiles for clothing, is greatly enhanced with GBM electrodes. Further work is required on GBM electrodes for motion artefact robustness, sensitivity, biocompatibility, polarization, longevity, and interaction between these factors is still required.