The mechanisms that affect the long-term fate of carbon dioxide in the subsurface are discussed with an emphasis on pore-scale imaging studies to study capillary trapping and dissolution processes in carbonates.  It is shown that capillary trapping can trap a significant fraction of the injected carbon dioxide even in heterogeneous carbonate formations.  The extension of the work to carbon dioxide storage into oil fields is discussed.  We demonstrate that at near-miscible conditions and in mixed-wet or oil-wet reservoirs the carbon dioxide is intermediate-wet and that water is the most non-wetting phase.  The implications for storage and recovery are discussed, as well as suggestions for field-scale modelling of three-phase flow processes.