We review recent progress that sheds light on the internal structure of general black holes. In particular, the asymptotic boundary conditions of general asymptotically flat black holes in four and five dimensions can be modified such that a conformal symmetry $SL(2,R)xSL(2,R)$ emerges. These subtracted geometries preserve the thermodynamic properties of the original black holes and are of the Lifshitz type, thus describing ``a black hole in the asymptotically conical box''. Such geometries can be obtained as a particular Harrison transformation on the original black holes. Recent efforts employ solution generating techniques to construct interpolating geometries between the original black hole and their subtracted geometries. The interpretation of these solution-generating transformations is shown to correspond to (pseudo)-dualities, showing that they correspond to combinations of T-dualities and Melvin twists. Upon uplift to one dimension higher, these dualities allow us to "untwist" general black holes to $AdS_3$ times a sphere.