The proliferation of distributed energy resources (DERs) and the deployment of advanced sensing and control technologies in electric power distribution systems calls for coordinated management of the grid’s resources. This has sparked a growing interest in optimization methods for large-scale unbalanced power distribution systems, with the goal of improving grid’s operational efficiency and resilience. The current fast-paced research in this domain is driven by the challenging mathematical problem of three-phase optimal power flow (OPF). This monograph introduces the state-of-the-art optimization methods applied to unbalanced power distribution systems for the provisioning of grid services from DERs. To that end, fundamentals of D-OPF methods are introduced along with the unique challenges and differences compared to the bulk grid and related aspects of computational complexity due to mutual coupling, unbalanced loading conditions, and control of legacy devices. Different models for formulating D-OPF problems are described in detail, as are methods for relaxing or approximating the formulations to achieve computational tractability. Finally, the use of D-OPF formulations to solve distribution-level operational problems via advanced distribution-level applications is described in detail. The specific applications discussed in this monograph include: (1) Volt-VAR control and Conservation Voltage Reduction using legacy voltage control devices and DERs, and (2) Solutions for Tomorrow’s Grid Reconfiguration and Restoration using DERs.