I discuss recent supergravity constructions of type IIB holographic interfaces in four-dimensional ${\cal N}=1$ and ${\cal N}=4$ field theories. I explain how each holographic interface can be compactified on a circle with an SL$(2,\mathbf{Z})$ monodromy leading to a novel AdS$_4$ supergravity solution. These AdS$_4$ backgrounds are argued to be dual to so-called J-fold superconformal field theories in three dimensions.