Silicon photonics allows optical waveguides to be integrated onto small chips and fabricated using scalable manufacturing. Integrated microresonators enhance the interaction between light and matter, enabling greater precision and control of light for a wide range of applications, including optical communications, sensing, and signal generation. This dissertation presents demonstrations of silicon photonic devices based on microresonators being used for switching, modulation, lasing, and four-wave mixing. Silicon waveguides have the potential for extremely high bandwidth density and can use multiplexing approaches similar to those emerging in fiber communications networks. Spatial multiplexing uses a new degree of freedom to expand bandwidth capacity in waveguides. Mode-multiplexed waveguides in silicon enable such high capacities and help relieve design constraints related to the use of multiple lasers. Here new functionalities for integrated mode-division multiplexing are presented. A fully-reconfigurable switch supporting multiple spatial modes and wavelengths is demonstrated. Additionally, an on-chip multimode link with three modes is demonstrated using integrated modulators. In another demonstration, a silicon nitride microresonator is used in a hybrid semiconductor laser cavity to provide resonant feedback. A narrow laser linewidth is achieved by leveraging the length enhancement of the microresonator. Coherent communications and other phase-sensitive applications rely on such narrow laser linewidths. In the final demonstration, which is a highlight of this dissertation, a fully-integrated frequency comb source is demonstrated. For the first time, a Kerr frequency comb is generated in an integrated microresonator without the need for an external laser. Soliton mode-locked combs are generated with extremely low power consumption, allowing battery operation of the compact comb source. This result could allow ubiquitous deployment of precise optical devices for sensing, spectroscopy, timing, and communications.