In contrast to conventional electrical machines, which typically consist of two components—excitation and armature units—FMMs incorporate an additional element, the modulation unit. This tripartite structure introduces multiple degrees of freedom in design, leading to a diverse range of FMM configurations. Despite the extensive exploration of various FMM types, including flux switching permanent magnet machines, flux reversal permanent magnet machines, and electrically excited doubly-salient machines, the underlying flux modulation mechanisms remain elusive. Consequently, the electromagnetic characteristics of these machines, characterized by high torque densities and low power factors, lack theoretical elucidation. Research findings applicable to one machine type do not necessarily translate to others, and a consistent framework for topological laws and design methodologies has yet to be established. This chapter elucidates five viable FMM types based on fundamental magnetic field constraints and the dynamics of the functional units. It further categorizes existing FMM topologies through the selection and integration of these units, thereby standardizing the framework and proposing novel FMM configurations, such as the flux modulation induction machine, for additional research.