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Microwave filters are indispensable passive devices for modern wireless communication systems. Nowadays, electromagnetic (EM) simulation-based design process is a norm for filter designs. Many EM-based design methodologies for microwave filter design have emerged in recent years to achieve efficiency, automation, and customizability. The majority of EM-based design methods exploit low-cost models (i.e., surrogates) in various forms and artificial intelligence techniques assist the surrogate modeling and optimization processes. Focusing on surrogate assisted microwave filters designs, this paper firstly analyzes the characteristic of filter design based on different design objective functions. Then, the state-of-the-art filter design methodologies are reviewed, including surrogate modeling (machine learning) methods and advanced optimization algorithms. Three essential techniques in filter designs are included: 1) Smart data sampling techniques; 2) Advanced surrogate modeling techniques. 3) Advanced optimization methods and frameworks. To achieve success and stability, they have to be tailored or combined together to achieve the specific characteristics of the microwave filters. Finally, new emerging design applications and future trends in filter design are discussed.

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