One of the most critical environmental challenges currently is the increase in atmospheric CO2 levels. Significant research efforts have been directed toward advanced porous materials, especially porous organic polymers (POPs), which are considered highly promising for CO2 capture due to their exceptional porosity, versatility of their structure, and remarkable physicochemical properties. Recent progress in POPs, particularly the crystalline class such as covalent triazine frameworks (CTFs) and covalent organic frameworks (COFs), has demonstrated considerable potential for CO2 capture. COFs, characterized by their well-ordered structures, exhibit remarkable properties including large surface areas and ease to tether surface functionalities. Interestingly, surface functionalization methods, such as the addition of amine (-NH2) groups and in situ modification with hydroxyl (-OH), carbonyl (-CHO) and carboxyl (-COOH) groups, have been found to significantly improve CO2 adsorption capacity of POPs. The advancement of COFs and CTFs, and generally POPs, offers a promising approach to tackling the challenges of CO2 capture, aiding efforts to lower greenhouse gas emissions and address environmental issues. This review explores the application of POPs for CO2 capture, focusing on the role of surface functionalization. Additionally, we examine the mechanisms of how functional groups enhance CO2 capture and categorize them accordingly. Various CO2 capture technologies are also discussed. Finally, we identify key challenges and future research directions, such as developing novel functionalization strategies, hybrid materials, and the application of machine learning.