Acinetobacter baumannii is a prevalent clinical pathogen commonly found to be multidrug-resistant (MDR), causing serious to life-threatening infections, particularly hospital-acquired infections with limited therapeutic options. The MDR phenotype developed against this critical pathogen is increasingly developed globally, reaching a pan-drug-resistant phenotype conferring non-susceptibility to all antimicrobials used in its treatment according to the standard guidelines. Therefore, it is critical to develop innovative treatment approaches, such as phage therapy, considering the rise in drug-resistant A. baumannii infections. In this review, we highlight and discuss the up-to-date antimicrobial resistance of A. baumannii, the use of phages, their limitations, and future perspectives in treating A. baumannii infections. In addition, the combination of phages with antimicrobials, preclinical and clinical studies including pharmacokinetics and pharmacodynamics properties have been discussed.