Multidrug-resistant (MDR) pathogens pose a well-recognized global health threat that demands effective solutions; the situation is deemed a global priority by the World Health Organization and the European Centre for Disease Prevention and Control. Therefore, the development of new antimicrobial therapeutic strategies requires immediate attention to avoid the ten million deaths predicted to occur by 2050 as a result of MDR bacteria. The repurposing of drugs as therapeutic alternatives for infections has recently gained renewed interest. As drugs approved by the United States Food and Drug Administration, information about their pharmacological characteristics in preclinical and clinical trials is available. Therefore, the time and economic costs required to evaluate these drugs for other therapeutic applications, such as the treatment of bacterial and fungal infections, are mitigated. The goal of this review is to provide an overview of the scientific evidence on potential non-antimicrobial drugs targeting bacteria and fungi. In particular, we aim to: (i) list the approved drugs identified in drug screens as potential alternative treatments for infections caused by MDR pathogens; (ii) review their mechanisms of action against bacteria and fungi; and (iii) summarize the outcome of preclinical and clinical trials investigating approved drugs that target these pathogens.