A theoretical study considering classical molecular dynamics simulations on Natural Deep Eutectic Solvents based on cineole and organic acids (malic, succinic, or lactic acid) and their behavior as a solvent for CO2 capture are reported. The nanoscopic properties of eutectic + CO2 mixtures in a wide composition range are studied, considering intermolecular forces, solvation, and the changes in the solvent properties upon CO2 absorption. Likewise, interfacial properties of the solvent in contact with vacuum and pure CO2 and flue gas–like gas phases were considered. The results on solvent–gas interfaces allowed the characterization of the mechanism of CO2 capture, considered as a two stages procedure started with the gas adsorption at the interphase followed by an interface to bulk solvent diffusion leading to the gas solvation in the fluid. The study probes the suitability of terpenoid–based natural eutectics for carbon capture operations, thus allowing green, low cost, and sustainable solvents.