Acinetobacter baumannii is a bacterium classified as priority 1 by the World Health Organization due to the rapid development of antibiotic resistance leading to many therapeutic failures. However, the existence of dormant bacterial subpopulations, like persister cells, may also partly explain these therapeutic failures. Persister cells are a bacterial subpopulation that may survive to high concentrations of antibiotics compared to isogenic individuals. This temporary and reversible phenotype may eventually lead to the development of new antibiotic resistance or to the recurrence of infection. Persister cells are often studied, but the mechanisms involved in their selection / formation are complex and often poorly described (toxin/antitoxin; second messengers; SOS response; phenyl acetic catabolic pathway; membranes). The mechanisms involved in the selection of persister cells are complex, and some appear to be species- or strain-specific. For example, some systems, such as antitoxin toxin, are described by others as directly involved in the formation of these cells. In fact, A. baumannii presents a great diversity of systems of antitoxin toxin. This review focuses on current advances in knowledge concerning the molecular mechanisms involved in the physiology of persister cells in A. baumannii, and the eradication strategies developed to combat this dormant subpopulation.