What are the characteristics of a triac and thyristor?

Triacs and thyristors can switch the flow of an electricity supply. Solid-state Relays use this function to switch AC power. Solid-state Relays that switch AC power thus have the characteristics of triacs and thyristors.

They are different from power transistors or power MOS FETs, because they are semiconductor devices they cannot turn themselves OFF. They can be turned ON with a gate signal to supply current but simply turning the gate signal OFF will not stop the current. The element will remain ON until the current flow reaches zero. 
This is an important aspect that must be considered to ensure safety in the system design, as well as the fact that semi-conductors are susceptible to breakdown caused by short-circuits.