Acinetobacter baumannii is a bacterium classified as ‘Critical’ by the World Health Organization due to the rapid development of antibiotic resistance leading to many therapeutic failures. However, the existence of persister bacterial subpopulations may also partly explain these therapeutic failures. Persister cells are a bacterial subpopulation that may survive to higher 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 making it important to study. The mechanisms involved in the selection of persister cells are multiple and complex involving toxin/antitoxin systems, second messengers, the SOS response, the phenyl acetic catabolic pathway or membranes modifications. Some of these mechanisms, like toxin/antitoxin systems presenting a great diversity, appear to be species- or strain-specific. 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.