Book excerpt: Optical traveling-wave resonator architectures have shown promise for the realization of many compact photonic functionalities in different research disciplines. Realizing these resonator structures in high-index contrast silicon enables dense and large scale integration of large arrays of functionalized resonators in a CMOS-compatible technology platform. Based on these motivations, the main focus of this Ph. D. research has been on the device physics, modeling, implementations, and applications of planar ultra-high Q silicon traveling-wave microresonators in a silicon-on-insulator (SOI) platform. Microdisk, microring, and racetrack resonators are the three general traveling-wave resonator architectures of interests that I have investigated in this thesis, with greater emphasis on microdisks. I have developed efficient tools for the accurate modeling of these resonators. The coupling to these resonators has been through a nano-waveguide side coupled to them. For this purpose, I have developed a systematic method for engineering a waveguide-resonator structure for optimum coupling. I have addressed the development of nanofabrication techniques for these resonators with efficient interaction with a nano-waveguide and fully compatible with active electronic integration. The outcome of the theoretical design, fabrication, and characterization of these resonators is a world-record ultra-high Q (3 x 106]) with optimum waveguide-resonator interaction. I have investigated the scaling of these resonators toward the ultimate miniaturization and its impact on different physical properties of the resonators. As a result of these investigations, I have demonstrated miniaturized Si microdisk resonators with radii of ~ 1.5 micron and Q> 105 with single-mode operation over the entire large free-spectral range. This is the highest Q (~ one order more than that in previously reported data) that has been obtained for a Si microdisk resonator with this size on a SiO2 substrate. I have employed these resonators for more advanced functionalities such as large-scale integration of resonators for spectroscopic and filtering applications, as well as the design of flat-band coupled-resonator filter structures. By proposing a systematic method of design, I have shown ultra-compact coupled-resonator filters with bandwidths ranging from 0.4 to 1 nm. I have theoretically and experimentally investigated the performance of ultra-high Q resonators at high powers and in the presence of nonlinearities. At high powers, the presence of two-photon absorption, free-carrier generation, and thermo-optic properties of silicon results in a rich dynamic in the response of the resonator. In both theory and experiment, I have predicted and demonstrated self-sustained GHz oscillation on the amplitude of an ultra-high Q resonator pumped with a continuous-wave laser.