Chronic kidney disease (CKD) affects about 10% of all populations worldwide, with about 2 million people requiring dialysis. Although patients with CKD are at high risk of cardiovascular disease and events, they are often underrepresented or excluded in clinical trials, leading to important knowledge gaps about how to treat these patients. KDIGO (Kidney Disease: Improving Global Outcomes) convened the fourth clinical Controversies Conference on the heart, kidney and vasculature in Dublin, Ireland, in February 2020, entitled Central and Peripheral Arterial Diseases in Chronic Kidney Disease. A global panel of multidisciplinary experts from the fields of nephrology, cardiology, neurology, surgery, radiology, vascular biology, epidemiology, and health economics attended. The objective was to identify key issues related to the optimal detection, management, and treatment of cerebrovascular diseases, central aortic disease, renovascular disease, and peripheral artery disease in the setting of CKD. This report outlines the common pathophysiology of these vascular processes in the setting of CKD, describes best practices for their diagnosis and management, summarizes areas of uncertainty, addresses ongoing controversial issues, and proposes a research agenda to address key gaps in knowledge that, when addressed, could improve patient care and outcomes.