Microwave filter is the key building block in the radio frequency (RF) system such as wireless communication and radar. Recently, silicon integrated microwave photonic filters (MPF) have been a hot research topic due to their capacities on integration, large bandwidth, excellent tunability and immunity to electromagnetic interference. In this paper, the operation principle of MPF is introduced firstly. Then, the latest research progresses of incoherent and coherent silicon integrated MPF are reviewed, and also the problems and challenges are analyzed. Finally, the main achievements of silicon integrated MPF up to now are summarized, and the next research orientations are discussed.