Carbon monoxide (CO) is a key material in C1 chemistry for chemical production and CO2 reduction, whereas in applications, such as H2 for fuel cells, its concentration must be kept below 0.2 ppm. Adsorption technology is useful for both CO removal and production to provide environmental sustainability for the energy and chemical industries. In this review, the CO adsorption performances of various adsorbents, such as activated carbons, zeolites, metal–organic frameworks, activated alumina, mesoporous silicas, and their modified adsorbents, are collected, and their physical and chemical properties and CO selectivities are summarized. Cu+ impregnation is a powerful and widely used modification method to enhance the CO adsorption of adsorbents. Therefore, the preparation methods and their effects on CO adsorption are also compared and reviewed. The data and analysis in this review can provide insights for the development of novel adsorbents and processes for CO removal and production.