Meeting the ambitious long-term temperature goal of the Paris Agreement necessitates far-reaching changes in the global energy system and economy. Understanding both physical constraints on this transition, as well as economic constraints on the deployment of various technologies, can help to assess what role carbon capture and storage (CCS) can play in achieving this transition over the remainder of the century. This chapter reviews the necessary physical climate science to understand the role of CCS in limiting warming. We describe how the concept of a finite “carbon budget” arises out of interactions between the carbon-cycle and the rest of the climate system. A clear physically-based requirement for achieving the long-term temperature goal of the Paris Agreement is the necessity of reaching global net-zero carbon dioxide emissions into the atmosphere. Based on this insight, we undertake a high-level but informative decomposition of Integrated Assessment Model (IAM) emissions reduction scenarios into contributions arising from the substitution of demand for carbon dioxide, and from the sequestration of carbon dioxide. In all scenarios that allow for the availability of CCS, the cost-effective solution offsets 20% or greater of business-as-usual end-of-century CO₂ emissions with CCS and/or negative emissions technologies. We highlight the need for the sequestered fraction of extracted carbon, a potentially useful climate policy measure, to rise to reach unity in order to limit warming to any value and describe a near-term schedule for increases in this fraction compatible with IAM-simulated cost-effective pathways that succeed in meeting the Paris Agreement long-term temperature goal.