The injection of CO2 into geological formations triggers inherently coupled thermo-hydro-chemo-mechanical processes. The reservoir pressure and temperature determine the CO2 density, the CO2-water interfacial tension, and the solubility of CO2 in water (hindered by salts and competing gases). The CO2-water interface experiences marked pinning onto mineral surfaces, and contact angles can range from the asymptotic advancing to receding values, in contrast to the single contact angle predicted by Young’s equation. CO2 dissolves in water to form carbonic acid and the acidified water dissolves minerals; mineral dissolution enhances porosity and permeability, triggers settlement, may couple with advection to form “wormholes”, produces stress changes and may cause block sliding and shear bands. Convective currents can emerge beneath the CO2 plume and sustain CO2 and mineral dissolution processes. On the other hand, mineralization is a self-homogenizing process in advective regimes. The crystallization pressure can exceed the tensile capacity of the host rock and create new surfaces or form grain-displacive lenses. Within the rock matrix, coupled reactive-diffusion-precipitation results in periodic precipitation bands. Adequate seal rocks for CO2 geological storage must be able to sustain the excess capillary pressure in the buoyant CO2 plume without experiencing open-mode discontinuities or weakening physico-chemical interactions. CO2 injection into depleted oil reservoirs benefits from time-proven seals; in addition, CO2 can mobilize residual oil to simultaneously recover additional oil through oil swelling, ganglia destabilization, the reduction in oil viscosity and even miscible displacement. Rapid CO2 depressurization near the injection well causes cooling under most anticipated reservoir conditions; cooling can trigger hydrate and ice formation, and reduce permeability. In some cases, effective stress changes associated with the injection pressure and cooling thermoelasticity can reactivate fractures. All forms of carbon geological storage will require large reservoir volumes to hold a meaningful fraction of the CO2 that will be emitted during the energy transition.