Cyber infrastructure will be a critical consideration in the development of next generation gravitational-wave detectors. The demand for data analysis computing in the 3G era will be driven by the high number of detections as well as the expanded search parameter space for compact astrophysical objects and the subsequent parameter estimation follow-up required to extract the nature of the sources. Additionally, there will be an increased need to develop appropriate and scalable computing cyberinfrastructure, including data access and transfer protocols, and storage and management of software tools, that have sustainable development, support, and management processes. This report identifies the major challenges and opportunities facing 3G gravitational-wave observatories and presents recommendations for addressing them. This report is the fourth in a six part series of reports by the GWIC 3G Subcommittee: i) Expanding the Reach of Gravitational Wave Observatories to the Edge of the Universe, ii) The Next Generation Global Gravitational Wave Observatory: The Science Book, iii) 3G R&D: R&D for the Next Generation of Ground-based Gravitational Wave Detectors, iv) Gravitational Wave Data Analysis: Computing Challenges in the 3G Era (this report), v) Future Ground-based Gravitational-wave Observatories: Synergies with Other Scientific Communities, and vi) An Exploration of Possible Governance Models for the Future Global Gravitational-Wave Observatory Network.