This dissertation aims to develop decision-making tools that aid power grid operators in mitigating extreme events. Two distinct areas are focused on: a) improving grid performance after a severe disturbance, and b) enhancing grid monitoring to facilitate timely preventive actions. The first part of the dissertation presents a proactive islanding strategy to split the bulk power transmission system into smaller self-adequate islands in order to arrest the propagation of cascading failures after an event. Heuristic methods are proposed to determine in what sequence should the island boundary lines be disconnected such that there are no operation constraint violations. The idea of optimal partitioning is further extended to the distribution network. A planning problem for determining which parts of the existing distribution grid can be converted to microgrids is formulated. This partitioning formulation addresses safety limits, uncertainties in load and generation, availability of grid-forming units, and topology constraints such as maintaining network radiality. Microgrids help maintain energy supply to critical loads during grid outages, thereby improving resilience. The second part of the dissertation focuses on wide-area monitoring using Phasor Measurement Unit (PMU) data. Strategies for data imputation and prediction exploiting the spatio-temporal correlation in PMU measurements are outlined. A deep-learning-based methodology for identifying the location of temporary power systems faults is also illustrated. As severe weather events become more frequent, and the threats from coordinated cyber intrusions increase, formulating strategies to reduce the impact of such events on the power grid becomes important; and the approaches outlined in this work can find application in this context. / Doctor of Philosophy / The modern power grid faces multiple threats, including extreme-weather events, solar storms, and potential cyber-physical attacks. Towards the larger goal of enhancing power systems resilience, this dissertation develops strategies to mitigate the impact of such extreme events. The proposed schemes broadly aim to- a) improve grid performance in the immediate aftermath of a disruptive event, and b) enhance grid monitoring to identify precursors of impending failures. To improve grid performance after a disruption, we propose a proactive islanding strategy for the bulk power grid, aimed at arresting the propagation of cascading failures. For the distribution network, a mixed-integer linear program is formulated for identifying optimal sub-networks with load and distributed generators that may be retrofitted to operate as self-adequate microgrids, if supply from the bulk power systems is lost. To address the question of enhanced monitoring, we develop model-agnostic, computationally efficient recovery algorithms for archived and streamed data from Phasor Measurement Units (PMU) with data drops and additive noise. PMUs are highly precise sensors that provide high-resolution insight into grid dynamics. We also illustrate an application where PMU data is used to identify the location of temporary line faults.