Renal involvement and kidney injury are common in COVID-19 patients, and the symptoms are more severe if the patient already has renal impairment. Renal involvement in COVID-19 is multifactorial, and the renal tubule is mainly affected, along with podocyte injury during SARS-CoV-2 infection. Inflammation, complement activation, hypercoagulation, and crosstalk between the kidney and lungs, brain, and heart are contributory factors. Kidney injury during the acute phase, termed acute kidney injury (AKI), may proceed to chronic kidney disease if the patient is discharged with renal impairment. Both AKI and chronic kidney disease (CKD) increase mortality in COVID-19 patients. Further, COVID-19 infection in patients suffering from CKD is more severe and increases the mortality rate. Thus, it is important to address both categories of patients, either developing AKI or CKD after COVID-19 or previously having CKD, with proper management and treatment. This review discusses the pathophysiology involved in AKI and CKD in COVID-19 infection, followed by management and treatment of AKI and CKD. This is followed by a discussion of the importance of screening and treatment of CKD patients infected with COVID-19 and future perspectives to improve treatment in such patients.