There is some disagreement as to the makeup of this genus. Depending on the taxonomist consulted, there are between 100 and 170 species of Alyssum. It includes annuals, herbaceous perennials and a few small shrubs that are native to the Mediterranean region, Asia and Northern Africa.

They are closely related to other genera including Lobularia and Aurinia. The name is from the Greek for "not or against" and "rage or madness" since the plant was once used against madness or bites from mad dogs.