Global investment in counteracting climate change has galvanized increasing interest in carbon capture and sequestration (CCS) as a versatile emissions mitigation technology. As decarbonization efforts accelerate, CCS can target the emissions of large point-source emitters, such as coal- or natural gas-fired power plants, while also supporting the production of renewable or low-carbon fuels. Furthermore, CCS can enable decarbonization of difficult-to-abate industrial processes and can support net CO removal from the atmosphere through bioenergy coupled with CCS or direct air capture. Here we review the development of porous materials as next-generation sorbents for CO capture applications. We focus on stream- and sector-specific challenges while highlighting case studies within the context of the rapidly shifting energy landscape. We conclude with a discussion of key needs from the materials community to expand deployment of carbon capture technologies.