The antimicrobial resistance crisis is an ongoing major threat to public health safety. Low- and middle-income countries are particularly susceptible to higher fatality rates and the economic impact of antimicrobial resistance (AMR). As an increasing number of pathogens emerge with multi- and pan-drug resistance to last-resort antibiotics, there is an urgent need to provide alternative antibacterial options to mitigate disease transmission, morbidity, and mortality. As identified by the World Health Organization (WHO), critically important pathogens such as Klebsiella and Pseudomonas species are becoming resistant to last-resort antibiotics including colistin while being frequently isolated from clinical cases of infection. Antimicrobial peptides are potent amino acid sequences produced by many life forms from prokaryotic, fungal, plant, to animal species. These peptides have many advantages, including their multi-hit mode of action, potency, and rapid onset of action with low levels of resistance being evident. These innate defense mechanisms also have an immune-stimulating action among other activities in vivo, thus making them ideal therapeutic options. Large-scale production and formulation issues (pharmacokinetics, pharmacodynamics), high cost, and protease instability hinder their mass production and limit their clinical application. This review outlines the potential of these peptides to act as therapeutic agents in the treatment of multidrug-resistant infections considering the mode of action, resistance, and formulation aspects. Clinically relevant Gram-positive and Gram-negative pathogens are highlighted according to the WHO priority pathogen list.