Global warming resulting from the emission of greenhouse gases, especially CO2, has become a widespread concern in the recent years. Though various CO2 capture technologies have been proposed, chemical absorption and adsorption are currently believed to be the most suitable ones for post-combustion power plants. The operation of the chemical absorption process is reviewed in this work, together with the use of absorbents, such as the ionic liquid, alkanolamines and their blended aqueous solutions. The major concerns for this technology, including CO2 capture efficiency, absorption rate, energy required in regeneration, and volume of absorber, are addressed. For adsorption, in addition to physical adsorbents, various mesoporous solid adsorbents impregnated with polyamines and grafted with aminosilanes are reviewed in this work. The major concerns for selection of adsorbent, including cost, adsorption rate, CO2 adsorption capacity, and thermal stability, are compared and discussed. More effective and less energy-consuming regeneration techniques for CO2-loaded adsorbents are also proposed. Future works for both absorption and adsorption are suggested.