According to a philosophy of Grothendieck, every good cohomology theory should have a six functor formalism. Arithmetic D-modules were introduced by Berthelot to provide the theory of rigid cohomology with exactly such a formalism. However, it is not clear that cohomology groups computed via the theory of arithmetic D-modules coincide with the analogous rigid cohomology groups. In this talk I will describe an 'overconvergent Riemann-Hilbert correspondence' that can be used to settle this question