Carbon geosequestration (CGS) has been identified as a key technology to reduce anthropogenic greenhouse gas emissions and thus significantly mitigate climate change. In CGS, CO is captured from large point-source emitters (e.g., coal fired power stations), purified, and injected deep underground into geological formations for disposal. However, the CO has a lower density than the resident formation brine and thus migrates upward due to buoyancy forces. To prevent the CO from leaking back to the surface, four trapping mechanisms are used: (1) structural trapping (where a tight caprock acts as a seal barrier through which the CO cannot percolate), (2) residual trapping (where the CO plume is split into many micrometer-sized bubbles, which are immobilized by capillary forces in the pore network of the rock), (3) dissolution trapping (where CO dissolves in the formation brine and sinks deep into the reservoir due to a slight increase in brine density), and (4) mineral trapping (where the CO introduced into the subsurface chemically reacts with the formation brine or reservoir rock or both to form solid precipitates). The efficiency of these trapping mechanisms and the movement of CO through the rock are strongly influenced by the CO-brine-rock wettability (mainly due to the small capillary-like pores in the rock which form a complex network), and it is thus of key importance to rigorously understand CO-wettability. In this context, a substantial number of experiments have been conducted from which several conclusions can be drawn: of prime importance is the rock surface chemistry, and hydrophilic surfaces are water-wet while hydrophobic surfaces are CO-wet. Note that CO-wet surfaces dramatically reduce CO storage capacities. Furthermore, increasing pressure, salinity, or dissolved ion valency increases CO-wettability, while the effect of temperature is not well understood. Indeed theoretical understanding of CO-wettability and the ability to quantitatively predict it are currently limited although recent advances have been made. Moreover, data for real storage rock and real injection gas (which contains impurities) is scarce and it is an open question how realistic subsurface conditions can be reproduced in laboratory experiments. In conclusion, however, it is clear that in principal CO-wettability can vary drastically from completely water-wet to almost completely CO-wet, and this possible variation introduces a large uncertainty into trapping capacity and containment security predictions.