Acinetobacter baumannii is considered one of the prioritized ESKAPE microorganisms for the research and development of novel treatments by the World Health Organization, especially because of its remarkable persistence and drug resistance. In this review, we describe how this can be acquired by the enzymatic degradation of antibiotics, target site modification, altered membrane permeability, multidrug efflux pumps, and their ability to form biofilms. Also, the evolution of drug resistance in A. baumannii, which is mainly driven by mobile genetic elements, is reported, with particular reference to plasmid-associated resistance, resistance islands, and insertion sequences. Finally, an overview of existing, new, and alternative therapies is provided.