Electrical power systems are increasing in size, complexity, as well as dynamics due to the growing integration of renewable energy resources, which have sporadic power generation. This necessitates the development of near real-time power system algorithms, demanding lower computational complexity regarding the power system size. Considering the growing trend in the collection of historical measurement data and recent advances in the rapidly developing deep learning field, the main goal of this paper is to provide a review of recent deep learning-based power system monitoring and optimization algorithms. Electrical utilities can benefit from this review by re-implementing or enhancing the algorithms traditionally used in energy management systems (EMS) and distribution management systems (DMS).