Microwave photonics (MWP) is an emerging issue concering the interaction between microwaves and optical waves. A variety of photonic technologies are investigated to enable and enhance functionalities in microwave systems which are usually very challenging when using pure electrical solutions. A fiber Bragg grating (FBG) is one of the key photonic devices in microwave photonics signal processing due to its unique features such as flexible spectral characteristics, low loss, light weight, compact footprint, and inherent compatibility with other fiber-optic devices. The recent development in FBG-based microwave photonics signal processing applications is discussed, with an emphasis on microwave photonic filters, microwave arbitrary waveform generation, microwave spectrum sensing and real-time FBG sensor interrogation. The limitations and potential solutions of FBG-based MWP system are also discussed.