Electrical activities inside the heart are immensely important for the functioning of this vital organ. In the pursuit of a scientific understanding of the processes and mechanisms in electro-physiology, computer simulations have become an established paradigm of research. Both the complex mathematical models and the extreme physiological details require huge-scale simulations, which nowadays see an increasing use of heterogeneous computing. That is, the computational power is delivered by more than one processor type. We will discuss some of the resulting challenges in programming and performance optimization. Successful applications from the domain of cardiac electro-physiology will be used to demonstrate the usefulness of heterogeneous computing. We will also take a peek into the future of heterogeneous computing through eX3: the brand-new national infrastructure for experimental exploration of exascale computing.