CO2 capture and geologic sequestration is one of the most promising options for reducing atmospheric emissions of CO2. Its viability and long-term safety, which depends on the caprock’s sealing capacity and integrity, is crucial for implementing CO2 geologic storage on a commercial scale. In terms of risk, CO2 leakage mechanisms are classified as follows: diffusive loss of dissolved gas through the caprock, leakage through the pore spaces after breakthrough pressure has been exceeded, leakage through faults or fractures, and well leakage. An overview is presented in which the problems relating to CO2 leakage are defined, dominant factors are considered, and the main results are given for these mechanisms, with the exception of well leakage. The overview includes the properties of the CO2–water/brine system, and the hydromechanics, geophysics, and geochemistry of the caprock-fluid system. In regard to leakage processes, leakage through faults or fracture networks can be rapid and catastrophic, whereas diffusive loss is usually low. The review identifies major research gaps and areas in need of additional study in regard to the mechanisms for geologic carbon sequestration and the effects of complicated processes on sealing capacity of caprock under reservoir conditions.