Microwave beamformer is one of the core components in phased array radar systems and 5G communication base stations. In recent years, silicon integrated microwave photonic beamformers have become one of the research hotspots in microwave photonics due to their advantages of large bandwidth, compact size, light weight, low loss, and anti-electromagnetic interference. In this paper, the basic principles and the key performance indices of microwave photonic beamforming systems are first introduced. Then, several integrated tunable optical true delay lines and optical beamforming network architectures that applied in the integrated microwave photonic beamformers in recent years are summarized. And also, the recent progresses in the integrated microwave photonic beamforming chips and the automation control and calibration methods are reviewed. Finally, the prospects of the future developments of silicon integrated microwave photonic beamformers are prospected.