Melanoma has emerged as a paradigm of a highly aggressive and plastic cancer, capable to co-opt the tumor stroma in order to adapt to the hostile microenvironment, suppress immunosurveillance mechanisms, and disseminate. In particular, oncogene- and aneuploidy-driven dysregulations of proteostasis in melanoma cells impose a rewiring of central proteostatic processes, such as the heat shock and unfolded protein responses, autophagy, and the endo-lysosomal system, to avoid proteotoxicity. Research over the past decade has indicated that alterations in key nodes of these proteostasis pathways act in conjunction with crucial oncogenic drivers to increase intrinsic adaptations of melanoma cells against proteotoxic stress, modulate the high metabolic demand of these cancer cells and the interface with other stromal cells, through the heightened release of soluble factors or exosomes. Here, we overview and discuss how key proteostasis pathways and vesicular trafficking mechanisms are turned into vital conduits of melanoma progression, by supporting cancer cell’s adaptation to the microenvironment, limiting or modulating the ability to respond to therapy and fueling melanoma dissemination.