The rapid growth of CO₂ emissions in the atmosphere has attracted great attention due to the influence of the greenhouse effect. Aerogels’ application for capturing CO₂ is quite promising owing to their numerous advantages, such as high porosity (~95%); these are predominantly mesoporous (20–50 nm) materials with very high surface area (>800 m²∙g⁻¹). To increase the CO₂ level of aerogels’ uptake capacity and selectivity, active materials have been investigated, such as potassium carbonate, K₂CO₃, amines, and ionic-liquid amino-acid moieties loaded onto the surface of aerogels. The flexibility of the composition and surface chemistry of aerogels can be modified intentionally—indeed, manipulated—for CO₂ capture. Up to now, most research has focused mainly on the synthesis of amine-modified silica aerogels and the evaluation of their CO₂-sorption properties. However, there is no comprehensive study focusing on the effect of different types of aerogels and modification groups on the adsorption of CO₂. In this review, we present, in broad terms, the use of different precursors, as well as modification of synthesis parameters. The present review aims to consider which kind of precursors and modification groups can serve as potentially attractive molecular-design characteristics in promising materials for capturing CO₂.