The overriding goal of the treatment of patients is its effectiveness and safety. However, all medications currently being used also exert some adverse pharmaceutical reactions, which may be regarded as an unintended but inevitable cost of pharmacotherapy. The kidney, as the main organ that eliminates xenobiotics, is an organ especially predisposed and vulnerable to the toxic effects of drugs and their metabolites during their excretion from the body. Moreover, some drugs (e.g., aminoglycosides, cyclosporin A, cisplatin, amphotericin B, and others) have a “preferential” nephrotoxicity potential, and their use is associated with an increased risk of kidney damage. Drug nephrotoxicity is, therefore, both a significant problem and a complication of pharmacotherapy. It should be noted that, currently, there is no generally recognized definition of drug-induced nephrotoxicity and no clear criteria for its diagnosis. This review briefly describes the epidemiology and diagnosis of drug-induced nephrotoxicity and characterizes its pathomechanisms, including immunological and inflammatory disturbances, altered kidney blood flow, tubulointerstitial injury, increased lithogenesis–crystal nephropathy, rhabdomyolysis, and thrombotic microangiopathy. The study also lists the basic drugs with nephrotoxicity potential and provides a short overview of the preventive methods for reducing the risk of drug-related kidney damage developing.