The Red Ajah of the Aes Sedai is the Ajah dedicated to controlling male channelers. The existence of the taint on saidin means that all such will eventually go mad. The Red Ajah instead gentles them. They are also particularly concerned with bringing down False Dragons when they spring up.
The sister at the top of the Ajah's internal hieararchy is known as the Highest.
In Crossroads of Twilight, it is first suggested that instead of gentling male channelers, Red sisters should start bonding with them.