Electric power systems provide the backbone of modern industrial societies. Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems. However, today' s power systems are suffering from everincreasing computational burdens in sustaining the expanding communities and deep integration of renewable energy resources, as well as managing huge volumes of data accordingly. These unprecedented challenges call for transformative analytics to support the resilient operations of power systems. Recently, the explosive growth of quantum computing techniques has ignited new hopes of revolutionizing power system computations. Quantum computing harnesses quantum mechanisms to solve traditionally intractable computational problems, which may lead to ultra-scalable and efficient power grid analytics. This paper reviews the newly emerging application of quantum computing techniques in power systems. We present a comprehensive overview of existing quantum-engineered power analytics from different operation perspectives, including static analysis, transient analysis, stochastic analysis, optimization, stability, and control. We thoroughly discuss the related quantum algorithms, their benefits and limitations, hardware implementations, and recommended practices. We also review the quantum networking techniques to ensure secure communication of power systems in the quantum era. Finally, we discuss challenges and future research directions. This paper will hopefully stimulate increasing attention to the development of quantum-engineered smart grids.