The discovery, commercialization, and regular administration of antimicrobial agents have revolutionized the therapeutic paradigm, making it possible to treat previously untreatable and fatal infections. However, the excessive use of antibiotics has led to develop resistance soon after their use in clinical practice, to the point of becoming a global emergency. The mechanisms of bacterial resistance to antibiotics are manifold, including mechanisms of destruction or inactivation, target site modification, or active efflux, and represent the main examples of evolutionary adaptation for the survival of bacterial species. The acquirement of new resistance mechanisms is a consequence of the great genetic plasticity of bacteria, which triggers specific responses that result in mutational adaptation, acquisition of genetic material, or alteration of gene expression, virtually producing resistance to all currently available antibiotics. Understanding resistance processes is critical to the development of new antimicrobial agents to counteract drug-resistant microorganisms. In this review, both the mechanisms of action of antibiotic resistance (AMR) and the antibiotic resistance genes (ARGs) mainly found in clinical and environmental bacteria will be reviewed. Furthermore, the evolutionary background of multidrug-resistant bacteria will be examined, and some promising elements to control or reduce the emergence and spread of AMR will be proposed.