As one of many actions required to mitigate climate change, carbon dioxide capture and sequestration (CCS) must be deployed quickly to avoid exceeding the atmospheric carbon budget that is expected to result in climate change effects that are very difficult to reverse. This chapter recognizes that regardless of motivating policy enacted, the degree of CCS deployment will be governed by cost effectiveness driven by thermodynamic efficiency of the CCS process as well as the cost to install and operate the system. First law analyses can provide perspectives on overall thermodynamic performance, while second law analyses can provide perspectives on performance expectations that are thermodynamically impossible to achieve. The cost of CCS technologies, in particular its relationship to the system size, differs amongst the basic CO₂ capture technology platforms. Understanding which thermodynamic improvements to make and for which size ranges a given technology platform is optimal is critical for efficient research and development. This chapter also provides perspectives on what capital and operating costs associated with the CCS system are required to meet the US Department of Energy CO₂ capture cost goal of $40 per tonne. Intelligent R&D guidance on thermodynamic and manufacturing improvements are expected to be required for all plant sizes.