An optical frequency comb (OFC) is a light source whose spectrum comprises of several sharp, equally spaced lines. They were originally developed more than two decades ago to simplify the measurement of optical frequencies in terms of precise atomic standards. OFC technology has progressed remarkably since the first demonstration and OFCs are now the cornerstones of modern-day frequency metrology, precision spectroscopy, astronomical observations, ultrafast optics and quantum information. While the current bulk mode-locked laser frequency comb has had great success in extending the scientific frontier, its use in real-world applications beyond the laboratory setting remains an unsolved challenge due to the relatively large size, weight and power consumption. Recently microresonator-based frequency combs have emerged as a candidate solution with chip-scale implementation and scalability. Microresonator platforms for comb generation are the subject of significant research efforts, which are primarily focused into three areas - comb stabilization, control over comb state generated and evolution paths and study of the comb formation dynamics. In this dissertation we focus on each of these three different areas. First, a novel internal phase-stabilized frequency microcomb that does not require nonlinear second-third harmonic generation nor optical external frequency references is demonstrated. It is shown that the optical frequency can be stabilized by control of two internally accessible parameters: an intrinsic comb offset and the comb spacing. Second, direct electrical control of microresonator parameters is achieved by coupling the gate-tunable optical conductivity of graphene to a silicon nitride photonic microresonator, and modulating its second- and higher-order chromatic dispersions by altering the Fermi level. This is then used to produce charge-tunable primary comb lines from 2.3 terahertz to 7.2 terahertz, coherent Kerr frequency combs, controllable Cherenkov radiation and controllable soliton states, all in a single microcavity. In addition, voltage-tunable transitions between soliton crystal states with defects with defects is demonstrated and mapped via ultrafast second-harmonic optical autocorrelation. Finally, novel ultrafast spectral and temporal measurement techniques are characterized and used to directly capture snapshots of the microresonator field at resolutions of less than 1 ps. These methods are applied to study spectral energy transfer, complex breathing dynamics, collective motion in soliton ensembles and the occurrence of extreme events from a chaotic background.