Circuit models for multiphase coupled inductors are summarized, compared, and unified. Multiwinding magnetic structures are classified into parallel-coupled structures and series-coupled structures. For parallel-coupled structures used for multiphase inductors, the relationships between a) inductance-matrix models, b) extended cantilever models, c) magnetic-circuit models, d) multiwinding transformer models, e) gyrator-capacitor models, and f) inductance-dual models are examined and discussed. These models represent identical physical relationships in the multiphase coupled inductors, but emphasize different physical aspects and offer distinct design insights. The circuit duality between the series-coupled structure and the parallel-coupled structure is explored. Design equations for interleaved multiphase buck converters based on these models are streamlined and summarized, and a simplified equation showing the relationships between current ripple with and without coupling is presented. The models and design equations are verified through theoretical derivation, SPICE simulation, and experimental measurements.