Distributed optimization algorithms may be used to coordinate large numbers of distributed energy resources (DERs) across transmission and distribution networks in the future power grid. These distributed algorithms have the potential to preserve privacy and autonomy while coordinating interconnected systems, and to improve scalability for large problems. However, there are challenges that must be addressed before implementing distributed algorithms for real-world system operation. First, distributed optimal power flow (OPF) requires repeated communication between controllers, which creates vulnerability to cyberattacks. Second, distributed OPF often takes many iterations to converge for large-scale power systems. Third, many traditional distributed optimization algorithms lack convergence guarantees for mixed-integer problems, which makes it difficult to solve problems with discrete decisions in a distributed manner. This dissertation explores methods to improve data security and reduce computation time for distributed OPF. First, this dissertation presents a machine learning-based method to detect and mitigate data integrity attacks on information shared between controllers. Second, it explores the impact of convergence tolerance, and introduces a bound tightening algorithm to prevent constraint violations at the distributed OPF operating point for a given convergence tolerance. Third, the dissertation reduces computation time by securely computing a distributed OPF warm start using privacy-preserving neural networks. The secure warm start can be combined with bound tightening to drastically reduce the number of iterations required to converge, thus reducing computation time and improving data security. Fourth, the dissertation explores making large-scale integrated transmission-distribution switching problems more tractable. To this end, the dissertation proposes developing reduced network models to be used with hierarchical optimization methods, and evaluates performance on realistic, large-scale synthetic distribution networks.