Antibiotics are powerful drugs used in the treatment of bacterial infections. The inappropriate use of these medicines has driven the dissemination of antibiotic resistance (AR) in most bacteria. Pseudomonas aeruginosa is an opportunistic pathogen commonly involved in environmental- and difficult-to-treat hospital-acquired infections. This species is frequently resistant to several antibiotics, being in the "critical" category of the WHO's priority pathogens list for research and development of new antibiotics. In addition to a remarkable intrinsic resistance to several antibiotics, P. aeruginosa can acquire resistance through chromosomal mutations and acquisition of AR genes. P. aeruginosa has one of the largest bacterial genomes and possesses a significant assortment of genes acquired by horizontal gene transfer (HGT), which are frequently localized within integrons and mobile genetic elements (MGEs), such as transposons, insertion sequences, genomic islands, phages, plasmids and integrative and conjugative elements (ICEs). This genomic diversity results in a non-clonal population structure, punctuated by specific clones that are associated with significant morbidity and mortality worldwide, the so-called high-risk clones. Acquisition of MGEs produces a fitness cost in the host, that can be eased over time by compensatory mutations during MGE-host coevolution. Even though plasmids and ICEs are important drivers of AR, the underlying evolutionary traits that promote this dissemination are poorly understood. In this review, we provide a comprehensive description of the main strategies involved in AR in P. aeruginosa and the leading drivers of HGT in this species. The most recently developed genomic tools that allowed a better understanding of the features contributing for the success of P. aeruginosa are discussed.