Herbal tea is really not "tea" at all. It is more properly called an "infusion" or a "tisane" – but you nearly always see it referred to as "tea". It contains no part of the camellia sinensis plant, but is made entirely from herbs, flowers, berries, spices or leaves. Because there is no "tea" in it, it has no caffeine.
Rooibos is also an herbal infusion. It comes from a plant that is native to South Africa, where it has been enjoyed for centuries. It has no caffeine and is very high in antioxidants.
Mate is an herbal infusion that, strangely enough, contains a "caffeine-like" compound that creates an effect much like caffeine does. It is native to South America and was traditionally used by people of the Andes to keep them warm and alert.