This chapter discusses some of the proposed mechanisms of voltage breakdown in solids, liquids, and gases with primary emphasis on transformer oil. This is because in oil-filled transformers, due to the higher dielectric constant of the solid insulation, the highest electric stress tends to occur in the oil. In addition, the breakdown stress of the oil is generally much lower than that of the solid insulation. The same situation occurs in dry-type transformers, however the breakdown mechanism in the gas is much better understood. The voltage distribution is then calculated throughout the windings, using a suitable electrical model together with the appropriate input such as a lightning impulse excitation. An electrode area or volume dependence of breakdown is usually explained by means of a weak link theory. According to this theory, there is some weak spot, imperfection, or mechanism based on the presence of imperfections that causes the failure.