Thanks to its compatibility with the current CMOS technology and its potential of seamless integration with electronics, silicon photonics has been attracting an ever-increasing interest in recent years from both the academia and industry. By applying silicon photonic technology in microwave photonics, on-chip integration of microwave photonic systems could be implemented with improved performance including a much smaller size, better stability and lower power consumption. This thesis focuses on developing silicon-based photonic integrated circuits for microwave photonic applications. Two types of silicon-based on-chip devices, waveguide Bragg gratings and optical micro-cavity resonators, are designed, developed, and characterized, and the use of the developed devices in microwave photonic applications is studied. After an introduction to silicon photonics and microwave photonics in Chapter 1 and an overview of microwave photonic signal generation and processing in Chpater2, in Chapter 3 a silicon-based on-chip phase-shifted waveguide Bragg grating (PS-WBG) is designed, fabricated and characterized, and its use for the implementation of a photonic temporal differentiator is experimentally demonstrated. To have a waveguide grating that is wavelength tunable, in Chapter 4 a tunable waveguide grating is proposed by incorporating a PN junction across the waveguide grating, to use the free-carrier plasma dispersion effect in silicon to achieve wavelength tuning. The use of a pair of wavelength-tunable waveguide gratings to form a wavelength-tunable Fabry-Perot resonator for microwave photonic signal processing is studied. Thanks to its electrical tunability, a high-speed electro-optic modulator, a tunable fractional-order photonic temporal differentiator and a tunable optical delay line are experimentally demonstrated. To increase the bandwidth of a waveguide grating, in Chapter 5 a linearly chirped waveguide Bragg grating (LC-WBG) is designed, fabricated and evaluated. By incorporating two LC-WBGs in two arms of a Mach-Zehnder interferometer (MZI) structure, an on-chip optical spectral shaper is produced, which is used in a photonic microwave waveform generation system based on spectral-shaping and wavelength-to-time (SS-WTT) mapping for linearly chirped microwave waveform (LCMW) generation. To enable the LC-WBG to be electrically tuned, in Chapter 6 a lateral PN junction is introduced in the grating and thus an electrically tunable LC-WBG is realized. By incorporating two tunable LC-WBGs in a Michelson interferometer structure, an electrically tunable optical spectral shaper is made. By applying the fabricated spectral shaper in an SS-WTT mapping system, a continuously tunable LCMW is experimentally generated. Compared with a waveguide Bragg grating device, an on-chip optical micro-cavity resonator usually has a much smaller dimension, which is of help to increase the integration density and reduce the power consumption. Different on-chip optical micro-cavity resonators are studied in this thesis. In Chapter 7, an on-chip symmetric MZI incorporating multiple cascaded microring resonators is proposed. By controlling the radii of the rings, the MZI could be designed to have a spectral response with a linearly-varying free spectral range (FSR), which could be used in photonic generation of an LCMW, and to have a multi-channel spectral response with identical channel spacing, which could be used in the implementation of an independently tunable multi-channel fractional-order temporal differentiator. To further reduce the footprint of an optical micro-cavity resonator, in Chapter 8 an ultra-compact microdisk resonator (MDR) with a single-mode operation and an ultra-high Q-factor is proposed, fabricated and evaluated, and its use for the implementation of a microwave photonic filter and an optical delay line is experimentally demonstrated. To enable the MDR to be electrically tunable, in Chapter 9 an electrically tunable MDR is realized by incorporating a lateral PN junction in the disk. The use of the fabricated MDR in microwave photonic applications such as a high-speed electro-optic modulator, a tunable photonic temporal differentiator and a tunable optical delay line is experimentally demonstrated.