Microwave photonic filters, which have attracted great research interest in the past few decades, are photonic subsystems carrying out functions of radio frequency (RF) filtering. Their advantages mainly include high bandwidth, low insertion loss, immunity to electromagnetic interference, etc. Quality factor (Q) value, which determines the performance of the frequency selectivity, is one of the most desired features of microwave photonic filters. Among various structures proposed so far to improve Q values of microwave photonic filters, multi-stage filters with cascaded structures have attracted lots of interests, which can increase the Q values greatly. The newly proposed structures on ultrahigh Q IIR microwave photonic filters with architectures of cascaded multi-stage filters are reviewed. Future directions of research in this area are also discussed.