A catalogue of insights from the fourth LIGO-Virgo-KAGRA observing run

Over the last decade, gravitational-wave science has developed from an era where a single detection was a Nobel-winning achievement to an (almost) everyday occurrence. The LIGO-Virgo-KAGRA (LVK) Collaboration's flagship scientific results are now their catalogues of detections, which include a comprehensive set of analysis results characterising the astrophysical properties of sources, and their implications for fundamental physics and cosmology. We review discoveries from the fourth observing run (O4) of the LVK network. The most recent catalogues each include about100 new detections. Among these new detections are remarkable single discoveries: the loudest signals detected so far, and sources unlike those seen before. However, significant advances in the field are coming from population-level analyses, leveraging the increasing sample size to infer constraints on the astrophysical distribution of merging compact binaries, potential deviations to general relativity, and the expansion rate of the Universe. Analyses of the latest data have revealed evidence for multiple subpopulations of sources. These observations provide a unique probe into the evolution of massive stars and the formation of coalescing binaries. Our understanding of gravitational-wave signals and their sources will continue to deepen with more observations. The final catalogue from O4 is due for release in December 2026, and future observing runs with even greater detector sensitivity are planned. These will bring even larger catalogues, and additional loud signals, continuing to advance gravitational-wave science.