Any formulation of the Divergence Formula involves two sets of regularity assumptions, one of geometric nature (regarding the underlying domain) and one of analytic nature (pertaining to the vector field involved).  The celebrated version proved by  De Giorgi and Federer, while allowing the domain to be rough, requires the intervening vector field to be smooth in the entire space. For many applications the latter condition is unreasonably restrictive, and the question arises as to what are the optimal assumptions on the vector field and domain for the Divergence Formula to hold in the case when the vector field in question may lack continuity. In this talk I will discuss recent progress on this topic.