Voltage breakdown limits many technologies that rely on strong electric fields. Although many kinds of voltage breakdown have been well-explained, voltage breakdown in vacuum--the sudden transition from vacuum insulation to vacuum arc--remains relatively poorly understood. Despite the importance of vacuum insulation, technology has hardly improved breakdown voltages in the last ninety years. This work describes experiments in vacuum breakdown, as well as computer simulations of the initial stages of breakdown. A better understanding of voltage breakdown could particularly benefit particle accelerators used for high energy physics experiments and radiation sources, which require the highest attainable electric fields in the microwave resonators that accelerate particles. Despite some differences, voltage breakdown in microwave resonators shares some features with breakdown in DC vacuum gaps (diodes). In both cases, the localized desorption of gas around an electron emission-source (e.g., field emission) could lead to breakdown. Analytical calculation shows that breakdown occurs when the product of the gas density and emission current exceed a critical value. Voltage breakdown in vacuum results from the interaction of the electric field and the electrodes. Using a scanning electron microscope, with energy dispersive x-ray spectroscopy (EDX) and Auger electron spectroscopy (AES) to identify surface constituents, we found that breakdown occurs often at the site of foreign particles on the cathode, usually leaving only a very small trace of the original material. At the breakdown site we frequently found small craters, surrounded by a large starburst-shaped pattern; surface analysis suggests that during breakdown, ions bombard the surface within the starburst region and sputter away surface contaminants and oxides. In general, particulate contamination on the cathode determines the breakdown voltage, independent of the cathode material or the thickness of the insulating surface oxide; however, the oxide thickness does change the nature of the starburst and the damage done to the surface during breakdown.