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Microwave photonics (MWPs) is an emerging interdisciplinary field, where photonics technologies are adopted to facilitate the generation, transmission, detection, and processing of signals at radio-wave, microwave, and millimeter-wave frequencies. Recently, the integrated photonic technology has demonstrated its capability to miniaturize photonic circuits on a single chip, which paves the way for next-generation integrated MWP signal processing systems having reduced size, weight, and power consumption (SWaP) specifications. In particular, by means of incorporating complementary metal-oxide-semiconductor (CMOS) electronic, optical, and optoelectronic components on a single integrated chip, silicon photonic circuits have brought new architectures and functionalities for MWP signal processing. This accelerates the evolution of MWPs from a single-use microwave signal processor toward a multitasking and cascadable MWP system, which is readily adaptable for a wide variety of uses and applications. In this review article, we provide an overview of the fundamental principle of the MWP signal processing topology. Developments in the microwave filtering technologies are reviewed with a focus on the integrated microwave filtering enhanced by optical phase equalization. We also review the recent progress and give an outlook for the future trend in MWP signal topologies, exploring the realization of multitasking and cascadable microwave signal processing systems based on silicon photonics. [ABSTRACT FROM AUTHOR]