The hospital environment constitutes a reservoir of opportunistic pathogens responsible for healthcare-associated infections (HCAI) such as Pseudomonas aeruginosa (Pa). Pa persistence within technological niches, the increasing emergence of epidemic high-risk clones in HCAI, the epidemiological link between plumbing strains and clinical strains, make it a major nosocomial pathogen. Therefore, understanding the mechanisms of Pa adaptation to hospital water systems would be useful in preventing HCAI. This review deciphers how copper resistance contributes to Pa adaptation and persistence in a hospital environment, especially within copper water systems, and ultimately to its success as a causative agent of HCAI. Numerous factors are involved in copper homeostasis in Pa, among which active efflux conferring copper tolerance, and copper-binding proteins regulating the copper compartmentalization between periplasm and cytoplasm. The functional harmony of copper homeostasis is regulated by several transcriptional regulators. The genomic island GI-7 appeared as especially responsible for the copper resistance in Pa. Mechanisms of copper and antibiotic cross-resistance and co-resistance are also identified, with potential co-regulation processes between them. Finally, copper resistance of Pa confers selective advantages in colonizing and persisting in hospital environments but also appears as an asset at the host/pathogen interface that helps in HCAI occurrence.