We study the response of a conserved current to external electromagnetic fields in a holographic system with boundaries using the recently proposed AdS/BCFT (boundary conformal field theory) framework. This, in particular, allows us to extract the Hall current, the Hall conductivity, plus some potentially novel transport coefficients, and relations among them. We also analyze the action of SL(2,ℤ) duality in the gravity bulk, which acts non-trivially on the conductivity of the BCFT. Finally we consider a type IIA string theory embedding of our setup. © SISSA 2012.