Most of the theory of D-modules has been developed only in characteristic zero. This includes holonomic modules. Some candidates for holonomic modules in characteristic p>0 have been proposed using definitions specific to characteristic p>0. The first characteristic-free definition of holonomicity was given in 2010 by the speaker, but only for modules over polynomial rings. In the talk I am going to describe an extension of this definition to arbitrary non-singular varieties. This is joint work with Wenliang Zhang.