Though electro-discharge machining (EDM) is in practical use for the last several decades, still several physical phenomena occurring during machining process are not well understood. For instance, it is well established that for higher material removal rate (MRR) in die sinking EDM of steel workpiece with copper tool the recommended polarity combination is positive tool and negative workpiece, usually called as normal polarity. However, in case of wire EDM for the same workpiece and tool materials combination, the opposite polarity combination is recommended for faster machining. Electro-discharge machining of steel and copper was done with both normal and reverse polarities for different pulse on-time. MRR was found to be lower in normal polarity than that in reverse polarity below certain pulse on-time, and beyond this MRR was higher in normal polarity. The crossover pulse on-time shifted towards higher values with increasing gap voltage. It was further observed that the crossover pulse on-time was higher for copper workpiece than that for steel at constant gap voltage. It was surprising to notice that the electrical discharge in both material combinations was equally regular for pulse on-time below crossover point in case of reverse polarity, but in case of normal polarity, while it was regular in copper, there was either no or infrequent discharge in steel. An attempt has been made to explain these observations analyzing various phenomena that could be involved in EDM, considering the behaviour of metal-debris (present in dielectric) interface, dynamics of space charge, and material properties, etc.