Microwave photonic filters have been characterized by low loss, light weight, broad bandwidth, good tunability, and immunity to electromagnetic interference, and these filters can overcome inherent electronic limitations. Fiber-based filters are inherently compatible with fiber-optic microwave systems and can provide connectivity with built-in signal conditioning. This review paper presents developments of microwave photonic filters based on semiconductor optical amplifier in the last few years. Challenges in system implementation for practical application are also discussed.