It is largely an open problem how to characterize the metrics on the n-sphere that are quasisymetrically or bi-lipschitzly equivalent to the standard metric, either locally or globally. By the double suspension theorem of Edwards and Cannon, there are polyhedral metrics on the n-sphere for n > 4 not bi-lipschitzly equivalent to the standard metric. Recently Semmes has constructed metrics in lower dimensions, n > 2, with good properties but without quasisymmetric coordinates. In this talk, I will discuss the above examples and problems about them. In particular, I will discuss recent joint work with Seppo Rickman which shows that in many cases the good metrics constructed by Semmes and others nevertheless admit ``coordinates'' by branched covers with geometric bounds.