The global rise of carbapenem-resistant Acinetobacter baumannii (CRAB) strains poses a critical challenge to healthcare systems due to limited therapeutic options and high mortality rates, especially in intensive care settings. This review explores the epidemiological landscape and molecular mechanisms driving carbapenem resistance, including the production of diverse beta-lactamases (particularly OXA-type enzymes), porin loss, efflux pump overexpression, and mutations in antibiotic targets. Emerging treatment strategies are discussed, such as the use of new beta-lactam–beta-lactamase inhibitor combinations (e.g., sulbactam–durlobactam), siderophore cephalosporins, next-generation polymyxins, as well as novel agents like zosurabalpin and rifabutin (BV100). Alternative approaches—including phage therapy, antimicrobial peptides, CRISPR-based gene editing, and nanoparticle-based delivery systems—are also evaluated for their potential to bypass traditional resistance mechanisms. Furthermore, advances in artificial intelligence and multi-omics integration are highlighted as tools for identifying novel drug targets and predicting resistance profiles. Together, these innovations represent a multifaceted strategy to overcome CRAB infections, yet their successful implementation requires further clinical validation and coordinated surveillance efforts. This analysis highlights the urgent need for continued investment in innovative treatments and effective resistance monitoring to limit the spread of CRAB and protect the effectiveness of last-line antibiotics.