Gigatonne scale geological storage of carbon dioxide and energy (such as hydrogen) will be central aspects of a sustainable energy future, both for mitigating CO₂ emissions and providing seasonal-based green energy provisions. In this Review, we evaluate the feasibility and challenges of expanding subsurface carbon dioxide storage into a global-scale business, and explore how this experience can be exploited to accelerate the development of underground hydrogen storage. Carbon storage is technically and commercially successful at the megatonne scale, with current projects mitigating approximately 30 Mt of CO₂ per year. However, limiting anthropogenic warming to 1.5°C could require gigatonnes of storage per year by 2050, and a scaleup from 2025 approaching rates of deployment that would be historic for energy technology. Scale-up is not limited by geology or engineering. Advances in understanding storage complex geology, subsurface fluid dynamics, and seismic risk underpin new engineering strategies including the development of multi-site, basin scale, storage resource management. Instead economic and societal contraints pose barriers to project development. Underground hydrogen storage, still in development, will face similar issues. Overcoming these barriers with strengthened financial incentives, and programs to address concerns inhibiting public acceptance, will enable the storage of CO₂ at climate relevant scales.