Rapidly increasing concentration of CO in the atmosphere has drawn more and more attention in recent years, and adsorption has been considered as an effective technology for CO capture from the anthropogenic sources. In this paper, the attractive adsorbents including activated carbons and amine-modified materials were mainly reviewed and discussed with particular attention on progress in the adsorbent preparation and CO adsorption capacity. Carbon materials can be prepared from different precursors including fossil fuels, biomass and resins using the carbonization-activation or only activation process, and activated carbons prepared by KOH activation with high CO adsorbed amount were reviewed in the preparation, adsorption capacity as well as the relationship between the pore characteristics and CO adsorption. For the amine-modified materials, the physical impregnation and chemical graft of polyethylenimine (PEI) on the different porous materials were introduced in terms of preparation method and adsorption performance as well as their advantages and disadvantages for CO adsorption. In the last section, the issues and prospect of solid adsorbents for CO adsorption were summarized, and it is expected that this review will be helpful for the fundamental studies and industrial applications of activated carbons and amine-modified adsorbents for CO capture.