Let M be a compact C manifold without boundary. Let Diff(M) be the group of C diffeomorphisms of M with the C topology. If r = 0 , this corresponds to the group of homeomorphisms of M. A C flow on M is a continuous group homomorphism (p:R->Diff(M), O^s^oo. In a natural way, C vector fields generate C flows and Lipschitz vector fields generate C° (topological) flows. We say that feDiff(M) embeds in a C flow, s^.r, iff is the map at time one of such a flow. Our main purpose is to announce results showing that few diffeomorphisms, in the sense of Baire category, embed in flows or are generated by vector fields with some mild differentiability or Lipschitz condition. Here we will prove only one of these results concerning flows generated by vector fields. Several authors have treated similar questions. For C diffeomorphisms of the circle, our last theorem follows from stronger results of Kopell [2] and it was also proved in [4], where more references can be found. The embedding of diffeomorphisms in topological flows was also considered in [5]. The author acknowledges very useful conversations with C. Pugh and M. Shub and several people at IMPA. We now show that with a mild assumption on the vector fields, the diffeomorphisms they possibly generate form a subset of first category in DiflP(Af)Fix a riemannian metric on M. Let x be a singularity for a vector field X. X is said to be Lipschitz at x if there exists a constant K>0 such that \X(y)\^Kd(x,y) for every y eM, where d(x,y) is the distance between x and y. Let % denote the set of C° vector fields on M that generate topological flows and are Lipschitz at the singularities.