The large symmetry group of string theory leads to new geometric structures of space-time, whose description remains very elusive. We will discuss a realization of such geometries obtained from six-dimensional, torus fibered heterotic compactifications with T-duality monodromy. These are described by a fibration of an auxiliary surface whose degenerations define stringy, ``non-geometric'' branes. We will study these objects by constructing F-theory dual models that admit Calabi-Yau resolutions, from which we can extract the low-energy physics. This leads to a set of 6D (1,0) SCFTs that we fully classify.