Cisplatin (cis-diamminedichloroplatinum (II), DDP) is an antineoplastic agent widely used in the treatment of solid tumors because of its extensive cytotoxic activity. However, the main limiting side effect of DDP use is nephrotoxicity, a rapid deterioration in kidney function due to toxic chemicals. Several studies have shown that epigenetic processes are involved in DDP-induced nephrotoxicity. Noncoding RNAs (ncRNAs), a class of epigenetic processes, are molecules that regulate gene expression under physiological and pathological conditions. MicroRNAs (miRNAs) are the most characterized class of ncRNAs and are engaged in many cellular processes. In this review, we describe how different miRNAs regulate some pathways leading to cell death by apoptosis, specifically the intrinsic apoptosis pathway. Accordingly, many classes of natural products have been tested for their ability to prevent DDP-induced apoptosis. The study of epigenetic regulation for underlying cell death is still being studied, which will allow new strategies for the diagnosis and therapy of this unwanted disease, which is presented as a side effect of antineoplastic treatment.