Abstract: The magnetic circuit theory stands as a pivotal theory for electromagnetic devices like electrical machines and transformers, furnishing indispensable tools for addressing intricate electromagnetic challenges and optimizing the performance of electromagnetic apparatus. In this paper, the historical development of magnetic circuit theory is first traced, providing insights into the valuable contributions made by earlier researchers towards refining magnetic circuit theories, including magnetic circuit parameters and their respective theoretical development. Additionally, their limitations and the challenges they encounter in practical applications are analyzed. On this basis, this paper pioneers the definition of magductance and hysteretance from the fundamental physical properties of magnetic circuit, establishes the vector magnetic circuit theory encompassing three core components (reluctance, magductance, and hysteretance), systematically and completely characterizes the three basic properties of magnetization, eddy current and hysteresis in the magnetic circuit, reveals the intrinsic connection between the virtual magnetic power and the electric power, and puts forward the magnetoelectric power law. An exhaustive comparative analysis with other magnetic circuit theories or modeling methods is conducted to illustrate their interconnections and differences. In order to show the applicative value of the vector magnetic circuit theory in science and engineering, four practical application scenarios are presented. Finally, the unique features of the proposed vector magnetic circuit theory are highlighted and the future research directions are prospected.