I will talk about the rational homotopy theory of Quillen and Sullivan. There is a Quillen adjunction between simplicial sets and commutative dg (=differential graded) algebras over the rationals that induces an equivalence between full subcategories of the respective homotopy categories whose objects are, on one side, simply connected rational spaces and, on the other, minimal dg-algebras. Roughly speaking, this means that the homotopy theory of rational spaces is reduced to differential homological algebra.