This document discusses techniques for reducing the operating costs of microgrids. It first provides background on microgrids and their architecture. Microgrids can operate connected to the main grid or in "island mode" disconnected from the main grid. The operating costs of a microgrid are typically higher when in island mode. The document then reviews various optimization algorithms and models that have been proposed to reduce microgrid operating costs when in island mode, such as stochastic models, dual decomposition methods, and resiliency-oriented scheduling models. It discusses challenges for microgrid planning, operation, and control due to the intermittent nature of renewable resources and need for economic optimization. The key techniques analyzed seek to minimize microgrid operating costs by optimizing scheduling of distributed energy