Abstract: I outline a proof, in the special case of groups, of Garrett Birkhoff's classical result that a nonempty class of algebraic structures of some fixed type is the model class of a set of identities if and only if it is closed under taking substructures, homomorphic images and direct products. Such classes are called varieties. I ponder free objects in varieties of groups. Time permitting I consider a question of Tarski relativized to certain varieties of groups.