Abstract Electrode geometry effects neglected by previous investigators of electrical breakdown in vacuum are shown to be significant in the range of 0 to 1 mm gap length, and 0 to 60 kV breakdown voltage for Al, Cu, and stainless steel electrodes. In particular, the curvature, area, and polarity effects reported here provide crucial tests of breakdown hypotheses. Convex electrodes of smaller radii of curvature have higher breakdown voltages that the more nearly plane electrodes. For a given radius of curvature, the electrodes of smaller cross-sectional area habe a higher breakdown voltage. A polarity effect is observed when the anode and cathode differ in cross-sectional area even though the electric field is approximately the same at both electrodes. The effects of material transfer, particle inertia, protrusion formation, erosion, patterned deposits, and micro-arcs are also reported. The major breakdown hypotheses are critically reviewed and their shortcomings as well as their successful aspects are pointed out. No hypothesis is found to be completely correct. A new hypothesis is introduced: that the energy available to initiate electrical breakdown is equal to all or a fraction of the capacitively stored energy of the electrodes. This hypothesis is shown to be capable of predicting at least qualitatively many of the experimental results, not predicted by previous hypotheses.