Multidrug resistance is a leading concern in public health. It describes a complex phenotype whose predominant feature is resistance to a wide range of structurally unrelated cytotoxic compounds, many of which are anticancer agents. Multidrug resistance may be also related to antimicrobial drugs, and is known to be one of the most serious global public health threats of this century. Indeed, this phenomenon has increased both mortality and morbidity as a consequence of treatment failures and its incidence in healthcare costs. The large amounts of antibiotics used in human therapies, as well as for farm animals and even for fishes in aquaculture, resulted in the selection of pathogenic bacteria resistant to multiple drugs. It is not negligible that the ongoing COVID-19 pandemic may further contribute to antimicrobial resistance. In this paper, multidrug resistance and antimicrobial resistance are underlined, focusing on the therapeutic options to overcome these obstacles in drug treatments. Lastly, some recent studies on nanodrug delivery systems have been reviewed since they may represent a significant approach for overcoming resistance.