The Grassmann algebras: derivations and identities

We survey some classical results on the polynomial identities satisfied by Grassmann algebras, with a list of recent new results on their derivations. Other new results concern the differential polynomial identities of the Grassmann algebra \(E\) of an infinite-dimensional vector space over a field of characteristic zero, arising under the derivation action of some Lie subalgebras of \(Der(E)\).