Abstract: We show that a generic extremal black hole in AdS is singular. In four dimensions, the horizon is replaced by a mild null singularity. That leaves significant imprints on the BH thermodynamics at sufficiently low temperatures. In five dimensions, that singularity becomes more serious. In particular, it makes RN AdS an unstable IR fixed point. Many new fixed points (described by near-horizon geometries) are constructed, and all of them are found to be unstable. Finally, we show that the higher curvature corrections to the extremal Kerr black hole make it singular as well. Furthermore, near-extremal black holes can have large yet finite tidal forces for infalling observers.