Drugs can impair the electrical activity of cardiomyocytes and induce cardiac arrhythmias with potentially lethal consequence. The current regulatory assays for predicting proarrhythmic risk are deterrents to drug development due to lack of specificity. As a consequence, the US FDA recently triggered the CiPA initiative for a radical overhaul of the drug safety paradigm based on human stem cell technology. In this talk, I give an introduction to computational drug cardiotoxicity testing with differential equations describing cardiac electrophysiology and highlight the association of bifurcations with drug induced early afterdepolarizations (EADs), which are precursors to cardiac arrhythmia at the cellular level. I will present recently published results that challenge the established hypothesis on EAD genesis and point to future topics of research.