The LIGO, VIRGO and KAGRA Gravitational-wave (GW) observatories are getting ready for their fourth observational period, O4, scheduled to begin in March 2023, with improved sensitivities and thus higher event rates. GW-related computing has both large commonalities with HEP computing, particularly in the domain of offline data processing and analysis, and important differences, for example in the fact that the amount of raw data doesn't grow much with the instrument sensitivity, or the need to timely generate and distribute "event candidate alerts" to EM and neutrino observatories, thus making gravitational multi-messenger astronomy possible. Data from the interferometers are exchanged between collaborations both for low-latency and offline processing; in recent years, the three collaborations designed and built a common distributed computing infrastructure to prepare for a growing computing demand, and to reduce the maintenance burden of legacy custom-made tools, by increasingly adopting tools and architectures originally developed in the context of HEP computing. So, for example, HTCondor is used for workflow management, Rucio for many data management needs, CVMFS for code and data distribution, and more. We will present GW computing use cases and report about the architecture of the computing infrastructure as will be used during O4, as well as some planned upgrades for the subsequent observing run O5.