In this dissertation, we introduce and study robust optimization models and decomposition algorithms in order to deal with the uncertainties such as terrorist attacks, natural disasters, and uncertain demand that are becoming more and more signicant in power systems operation and planning. An optimal power grid hardening problem is presented as a defender-attacker-defender (DAD) sequential game and solved by an exact decomposition algorithm. Network topology control, which is an eective corrective measure in power systems, is then incorporated into the defender-attacker-defender model as a recourse operation for the power system operator after a terrorist attack. Computational results validate the cost-eectiveness of the novel model. In addition, a resilient distribution network planning problem (RDNP) is proposed in order to coordinate the hardening and distributed generation resource placement with the objective of minimizing the distribution system damage under uncertain natural disaster events. A multi-stage and multi-zone based uncertainty set is designed to capture the spatial and temporal dynamics of a natural disaster as an extension to the N-K worst-case network interdiction approach. Finally, a power market day-ahead generation scheduling problem, i.e., robust unit commitment (RUC) problem, that takes account of uncertain demand is analyzed. Improvements have been made in achieving a fast