A V-functor is Cauchy dense when the counit of the profunctor adjunction it induces is an isomorphism. For metric spaces, this is exactly a short map whose image is topologically dense in its codomain. In this talk, I will review this notion and Lucatelli Nunes and Sousa's characterisation of the Cauchy dense V-functors as the lax epimorphisms in V-Cat when V is symmetric monoidal closed. I will explain why fully faithful Cauchy dense functors are intimately linked to Cauchy completion and Morita equivalence. We will also look at the one-object case, and see how the Cauchy dense maps of monoids in V tend to coincide with the epimorphisms, but not always.