Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a new homotopy theory for these algebras which let us extend with full generality the classical Quillen approach to rational homotopy theory of simply connected spaces. I will be exposing some aspect of this theory. Special emphasis will be given to the new model category structure for (complete) differential graded Lie algebras whose core lies in the construction of the "Eckmann-Hilton dual" of the classical differential forms on the standard simplices. In fact, the non-existence of this object in the Lie setting has puzzled (rational) homotopy theorists since the beginning of the subject. Joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.