Given a Lipschitz vector field, the classical Cauchy-Lipschitz theory gives existence, uniqueness and regularity of the associated ODE flow. In recent years, much attention has been devoted to extensions of such theory to cases in which the vector field is less regular than Lipschitz, but still belongs to some "weak differentiability classes". In this talk, I will review the main points of an approach involving quantitative estimates for flows of Sobolev vector fields (joint work with Camillo De Lellis) and describe further extensions to a case involving singular integrals of L1 functions (joint work with Francois Bouchut) and to a case endowed with a "split structure" (joint work with Anna Bohun and Francois Bouchut).