Microwave photonic (MWP) signal processing has attracted strong interest due to its unique advantages such as large operational bandwidth and immunity against electromagnetic interference. Recently, fast-growing markets in 5G wireless networks and the Internet of Things have become a strong thrust to the development of MWP signal processing. They are expected to benefit from MWPs with its capabilities to achieve a high time-bandwidth product in the transmission of microwave or millimeter-wave signals. Conventional MWP systems are composed of discrete optoelectronic devices and fiber-based components, which are usually bulky and power-hungry, making them inferior to the commercial RF electronic devices. It is therefore imperative to realize compact integrated MWP systems with reduced cost, size, weight and power consumption. While Moore's Law is approaching its limit to drive the evolution of electronic circuits, the silicon photonic integration platform, which features high compatibility with the standard CMOS processes, emerges as a promising solution. By incorporating both electronics and optics components on a single integrated chip, silicon photonic circuits ensure the unique characteristics of MWP signal processing such as wide bandwidth and high configurability are fully utilized, thus promoting the performance of integrated MWP signal processors. In this thesis, the applications of integrated silicon photonics on key MWP building blocks are investigated. The investigation is focused on the applications of microring resonators fabricated on SOI platform, which exhibit excellent compactness due to their inherent resonance effect and strong light confinement of the waveguide. The MWP building blocks we explore include an integrated optical single sideband modulator, a frequency tunable microwave filter for amplitude control and a photonic-assisted microwave frequency measurement system.