This paper reports studies on CO2 capture technologies and presents the mathematical modeling, simulation, and optimization of adsorption-based process alternatives, namely, pressure swing adsorption (PSA) and vacuum swing adsorption (VSA). Each technology includes feed dehydration, capture of at least 90% of CO2 from the feed, and compression to almost pure CO2 for sequestration at 150 bar. Each process alternative is optimized over a range of feed CO2 compositions and flow rates. A superstructure of alternatives is developed to select the optimum dehydration strategy for feed to each process. A four-step process with pressurization, adsorption in multiple columns packed with 13X zeolite, N-2 purging, and product recovery at moderate to low vacuum is configured. A nonlinear algebraic and partial differential equation (NAPDE) based nonisothermal adsorption model is used, which is fully discretized and solved via a kriging model. Explicit expressions for costs as functions of feed flow rate and CO2 composition are also developed for the PSA- and VSA-based CO2 capture and compression for the first time. Furthermore, a cost-based comparison of four leading CO2 capture technologies, namely, absorption-, membrane-, PSA-, and VSA-based processes, is presented over a range of flue gas compositions and flow rates. This enables selection of the most cost-effective CO2 capture and storage (CCS) technology for diverse emission scenarios. Results indicate that CO2 can be captured with the least cost using a MEA-based chemical absorption when the feed CO2 composition is less than 15-20%. For higher CO2 compositions, VSA is the preferred process.