The classical Maurer Cartan equation (aka the integrability or master equation) arises in deformation theory via the philosophy that deformation problems are (usually) controlled by a differential graded Lie algebra. However, that dgLa is determined only up to equivalence as an L-infty algebra. Thus the Maurer Cartan equation should be generalized to include the L-infty structure. This was implicit in the `cahier secret' of Schlessinger and Stasheff and has had a curious development since then.