What is the difference between "forward" and "reverse" voltages when working with diodes and LEDs?

I realize this question is answered elsewhere on the interwebs such as wikipedia, but I am looking for a short summary that is less of a technical discussion and more a useful tip to someone using diodes in a hobby circuit.

The forward voltage is the voltage drop across the diode if the voltage at the anode is more positive than the voltage at the cathode (if you connect + to the anode).

You will be using this value to calculate the power dissipation of the diode and the voltage after the diode.

The reverse voltage is the voltage drop across the diode if the voltage at the cathode is more positive than the voltage at the anode (if you connect + to the cathode).

This is usually much higher than the forward voltage. As with forward voltage, a current will flow if the connected voltage exceeds this value. This is called a "breakdown". Common diodes are usually destroyed but with Z and Zener diodes this effect is used deliberately.
