Resisting cell death is a hallmark of cancer. Disturbances in the execution of cell death programs promote carcinogenesis and survival of cancer cells under unfavorable conditions, including exposition to anti-cancer therapies. Specific modalities of regulated cell death (RCD) have been classified based on different criteria, including morphological features, biochemical alterations and immunological consequences. Although melanoma cells are broadly equipped with the anti-apoptotic machinery and recurrent genetic alterations in the components of the RAS/RAF/MEK/ERK signaling markedly contribute to the pro-survival phenotype of melanoma, the roles of autophagy-dependent cell death, necroptosis, ferroptosis, pyroptosis, and parthanatos have recently gained great interest. These signaling cascades are involved in melanoma cell response and resistance to the therapeutics used in the clinic, including inhibitors of BRAF mut and MEK1/2, and immunotherapy. In addition, the relationships between sensitivity to non-apoptotic cell death routes and specific cell phenotypes have been demonstrated, suggesting that plasticity of melanoma cells can be exploited to modulate response of these cells to different cell death stimuli. In this review, the current knowledge on the non-apoptotic cell death signaling pathways in melanoma cell biology and response to anti-cancer drugs has been discussed.