A variety of marketed drugs belonging to various therapeutic classes are known to cause nephrotoxicity. Nephrotoxicity can manifest itself in several forms depending on the specific site involved as well as the underlying pathophysiological mechanisms. As they often coexist with other pathophysiological conditions, the steps that can be taken to treat them are often limited. Thus, drug-induced nephrotoxicity remains a major clinical challenge. Prior knowledge of risk factors associated with special patient populations and specific classes of drugs, combined with early diagnosis, therapeutic drug monitoring with dose adjustments, as well as timely prospective treatments are essential to prevent and manage them better. Most incident drug-induced renal toxicity is reversible only if diagnosed at an early stage and treated promptly. Hence, diagnosis at an early stage is the need of the hour to counter it. Significant recent advances in the identification of novel early biomarkers of nephrotoxicity are not beyond limitations. In such a scenario, mathematical modeling and simulation (M&S) approaches may help to better understand and predict toxicities in a clinical setting. This review summarizes pathophysiological mechanisms of drug-induced nephrotoxicity, classes of nephrotoxic drugs, management, prevention, and diagnosis in clinics. Finally, it also highlights some of the recent advancements in mathematical M&S approaches that could be used to better understand and predict drug-induced nephrotoxicity.