In this talk we present some recent results about additive group actions on(non-necessarily affine)algebraic varieties that generalize the usual description of additive group actions on affine varieties.In particular,in the first part of this talk,we provide a characterization of additive group actions on a wide class of algebraic varieties in terms of a certain type of integrable vector fields.In the second part,if X is an algebraic variety such that Aut(X)is an algebraic group,we show how this characterization allows us to compute the connected component of Aut(X).We also show how this computations is realized in the case where the maximal torus T(∈)Aut(X)is such that dimT = dimX or dimT = dimX-1.Different parts of this talk are issued from joint works with A.Dubouloz; and I.Arzhantsev,J.Hausen and E.Herppich.