Patients undergoing transcatheter aortic valve replacement (TAVR) often have concomitant coronary artery disease (CAD) which may adversely affect prognosis. There is uncertainty about the benefits and the optimal timing of revascularization for such patients. There is currently clinical equipoise regarding the management of concomitant CAD in patients undergoing TAVR. Some centers perform routine revascularization with percutaneous coronary intervention (PCI) (either before or after TAVR), while others follow an alternative strategy of medical management. The potential benefits and optimal timing of PCI in these patients are unknown. As TAVR expands to lower risk patients, and potentially becomes the preferred therapy for the majority of patients with severe aortic stenosis, the optimal management of concomitant coronary artery disease will be of increasing importance. The COMPLETE TAVR study will determine whether, on a background of guideline-directed medical therapy, a strategy of complete revascularization involving staged PCI using drug eluting stents to treat all suitable coronary artery lesions is superior to a strategy of medical therapy alone in reducing the composite outcome of Cardiovascular Death, new Myocardial Infarction, Ischemia-driven Revascularization or Hospitalization for Unstable Angina or Heart Failure. The study will be a randomized, multicenter, open-label trial with blinded adjudication of outcomes. Patients will be screened and consented for elective transfemoral TAVR and randomized within 96 hours of successful balloon expandable TAVR. Complete Revascularization: Staged PCI using third generation drug eluting stents to treat all suitable coronary artery lesions in vessels that are at least 2.5 mm in diameter and that are amenable to treatment with PCI and have a ≥70% visual angiographic diameter stenosis. Staged PCI can occur any time from 1 to 45 days post successful transfemoral TAVR. Vs. Medical Therapy Alone: No further revascularization of coronary artery lesions. All patients, regardless of randomized treatment allocation, will receive guideline-directed medical therapy consisting of risk factor modification and use of evidence-based therapies. The COMPLETE TAVR study will help address the current lack of evidence in this area. It will likely impact both the global delivery of health care and the management and clinical outcomes of all patients undergoing TAVR with concomitant CAD.