It is quite challenging to understand the details of the complex mechanisms involved in the swelling processes of clays such as montmorillonite as a function of relative humidity (RH), and the adsorption and transport processes of CO2 and CH4 in swelling clays. Here we present a review of the molecular simulation results for the swelling clay systems which not only compare well with the experimental data but also provide deep insights into the details of these mechanisms. The presence of CO2 and CH4 hardly affects the distribution and mobility of the interlayer water and ions in these systems. Under all conditions, the stable basal d-spacing was mainly determined by the type of counterion present in the interlayer region and the amount of water in each hydration state was almost independent of the RH and the layer charge. The uptake of CH4 in the 1W state of the Na-clay was much smaller compared to that of CO2. The adsorbate mobility generally increased with increasing hydration/RH because of the associated swelling of the interlayer region. Interestingly, the uptake of CO2 in the high-charge clay was dramatically decreased, and the mobility of CO2 in each hydration state was almost independent of the type of cation. The preferential adsorption of CO2 over CH4 plays an important role in the diffusion processes. Such an understanding is important for the successful mitigation of climate change via storage of anthropogenic CO2 in geological formations.