The intrinsic and acquired resistance of Mycobacterium abscessus to commonly used antibiotics limits the chemotherapeutic options for infections caused by these mycobacteria. Intrinsic resistance is attributed to a combination of the permeability barrier of the complex multilayer cell envelope, drug export systems, antibiotic targets with low affinity and enzymes that neutralize antibiotics in the cytoplasm. To date, acquired resistance has only been observed for aminoglycosides and macrolides, which is conferred by mutations affecting the genes encoding the antibiotic targets (rrs and rrl, respectively). Here we summarize previous and recent findings on the resistance of M. abscessus to antibiotics in light of what has been discovered for other mycobacteria. Since we can now distinguish three groups of strains belonging to M. abscessus (M. abscessus sensu stricto, Mycobacterium massiliense and Mycobacterium bolletii), studies on antibiotic susceptibility and resistance should be considered according to this new classification. This review raises the profile of this important pathogen and highlights the work needed to decipher the molecular events responsible for its extensive chemotherapeutic resistance.