If we hook up a diode in a simple circuit with a variable voltage source and a current-limiting resistor, we can measure the current I through the diode when a given voltage V is applied across it. For an ideal diode, no current at all passes when the voltage is less than zero: the diode completely prevents reverse current flow. For small positive voltage (“forward bias,” or sometimes “foward voltage”), a tiny amount of current may flow, and a very large amount of current will flow above a given threshold. The amount of current that flows is actually exponential with increasing voltage.
The threshold where an appreciable amount of current flows is typically around 0.7 V for simple semiconductor diodes, but may be as low as 0.15 V for Schottky diodes, or as high as 4 V for certain types of LEDs.Of course, no diode is truly ideal. In real diodes, when the voltage is reversed, a very small amount of current (leakage) may flow. And, more significantly, each diode is rated for a certain maximum amount of reverse voltage. If you apply voltage more negative than that limit, the diode will undergo “reverse breakdown”
and begin to conduct a significant amount of current, but backwards from the normal direction of diode current flow. For a regular diode, we would say that the diode has failed if it begins to conduct current in that direction.
Aside: The actual physics of what happens at breakdown is quite interesting; two separate effects, the Zener effect and Avalanche breakdown both contribute to this behavior.