Cardiovascular event rates are high in patients with chronic kidney disease (CKD), increasing with deteriorating kidney function, highest in CKD patients on dialysis, and improve with kidney transplantation (KTx). The cardiovascular events in CKD patients such as myocardial infarction and heart failure are related to abnormalities of vascular and cardiac structure and function. Many studies have investigated the structural and functional abnormalities of the heart and blood vessels in CKD, and the changes that occur with KTx, but the evidence is often sparse and occasionally contradictory. We have reviewed the available evidence and identified areas where more research is required to improve the understanding and mechanisms of these changes. There is enough evidence demonstrating improvement of left ventricular hypertrophy, except in children, and sufficient evidence of improvement of left ventricular function, with KTx. There is reasonable evidence of improvement in vascular function and stiffness. However, the evidence for improvement of vascular structure and atherosclerosis is insufficient. Further studies are necessary to establish the changes in vascular structure, and to understand the mechanisms of vascular and cardiac changes, following KTx.