Off-pump coronary artery revascularization requires a unique skill set and a different conduct of operation compared with on-pump coronary artery bypass. Not only must the surgeon perform anastomoses on the beating heart, but he/she must understand the hemodynamic consequences of cardiac positioning and stabilization, the effects of regional ischemia on hemodynamic function, contractility, and arrhythmias, and the importance of anesthesia and grafting sequence given variants of anatomy and clinical conditions. Given these differences, the ability to teach off-pump coronary artery bypass to residents and surgeons places unique demands on the teaching surgeon. In this article, we review the available literature about the safety and efficacy of teaching off-pump coronary artery bypass to residents, discuss the fundamentals for training residents, and review the future of simulation and new training paradigms and the impact this will have on current training methods.