Zener diodes are semiconductor devices designed to function in the reverse direction by allowing current to flow when a breakdown voltage is reached. They can regulate voltage in circuits and are used for applications like voltage regulation, signal clamping, voltage references, and overvoltage protection. Key specifications for Zener diodes include their breakdown voltage which can range from 2.4V to 1kV, and their maximum current rating. Circuits using Zener diodes provide advantages like low cost voltage stabilization but also have disadvantages like wasting electricity during voltage regulation.