Exploring novel electric machines (EMs) with high efficiency, high torque density, and low cost is always an interesting research topic. In recent decades many different types of new EMs have emerged. Among others, these machines include a basic flux-modulated motor which uses the variation of magnetic reluctance to produce constant torque, a vernier motor which has special slot combinations, a doubly-fed magnetic reluctance machine which has two sets of windings on its stator, a flux-switching motor which has permanent magnets (PMs) on its stator, a dual-PM-excited motor with PMs on both rotor and stator. These machines have their own merits in specific applications. In this presentation, the internal relationships and operating mechanisms of these machines will be scrutinized and all these machines will be summarized as general flux-modulated machines, as they all employ non-uniform magnetic reluctance to modulate their magnetic flux to produce constant torque. A general theory to explain the operating principle of all these machines will be proposed. The examples of its applications for developing novel electric machines will be presented.