I will describe recent progress in our understanding of unusual quantum critical phenomena that lie outside the standard Landau paradigm.  Crucial related input into these quantum critical points has come from the study of gapped topological phases of matter and from the understanding of dualities of quantum field theories. I will highlight these connections and describe several new results on quantum critical points in 3+1-dimensional systems.  Based on this understanding, I will describe an interesting possible 3+1-D field theory duality.