We introduce a notion of constructibility for etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We use the work of R. Huber to define an adic Verdier dual and investigate the extent to which we have a 6-functor formalism in this context. We attempt to classify those sheaves which are reflexive with respect to the adic Verdier dual. This is joint work with John Weilliaveetil.