The cryogenic carbon capture (CCC) process is a promising post-combustion CO2 removal method. This method is very novel compared with conventional and well-developed methods. However, cryogenic carbon capture is not yet commercially available despite its techno-economic benefits. Thus, a model-based design approach for this process can provide valuable information. This paper will first introduce the cryogenic carbon capture process. Then, a comprehensive lit-erature overview that focuses on different methods for modeling the process at the component level will be given. The modelling methods which are deemed most effective are presented more in depth for each of the key system components. These methods are compared with each other in terms of complexity and accuracy and the simplest methods with an acceptable level of precision for modelling a specific component in the CCC process are recommended. Furthermore, potential research areas in modeling and simulation of the CCC process are also highlighted.