Combating antimicrobial resistance (AMR) is among the 10 global health issues identified by the World Health Organization (WHO) in 2021. While AMR is a naturally occurring process, the inappropriate use of antibiotics in different settings and legislative gaps has led to its rapid progression. As a result, AMR has grown into a serious global menace that impacts not only humans but also animals and, ultimately, the entire environment. Thus, effective prophylactic measures, as well as more potent and non-toxic antimicrobial agents, are pressingly needed. The antimicrobial activity of essential oils (EOs) is supported by consistent research in the field. Although EOs have been used for centuries, they are newcomers when it comes to managing infections in clinical settings; it is mainly because methodological settings are largely non-overlapping and there are insufficient data regarding EOs’ in vivo activity and toxicity. This review considers the concept of AMR and its main determinants, the modality by which the issue has been globally addressed and the potential of EOs as alternative or auxiliary therapy. The focus is shifted towards the pathogenesis, mechanism of resistance and activity of several EOs against the six high priority pathogens listed by WHO in 2017, for which new therapeutic solutions are pressingly required.