The science of ultra-high energy cosmic rays after 20 years of operation of the Pierre Auger Observatory

For over twenty years, the Pierre Auger Observatory has been at the forefront of ultra-high-energy cosmic ray (UHECR) research. Its emblematic hallmark is a \textit{hybrid} design: UHECRs are detected through complementary techniques that observe the extensive air showers (EASs) they produce. The combined analysis of multi-detector data has enabled high-precision, high-statistics studies of the energy spectrum, mass composition, and arrival direction distribution of UHECRs. This contribution summarizes the current understanding of UHECRs. While no individual sources have been pinpointed, the extragalactic origin of cosmic rays above 8~EeV has been confirmed, and higher-energy observations are beginning to trace them back to nearby astrophysical sites. Additionally, the stringent upper limits established on ultra-high-energy neutrino and gamma ray fluxes provide important constraints for multi-messenger astrophysics and physics beyond the Standard Model (BSM).