There is a very well developed theory of uniform rectifiability in Rn (due to David, Semmes, Jones and others). There are now several results of similar nature for metric spaces. We will recall/explain several Euclidean results and then go on to their counterparts for a general metric space. We will also discuss some parts of the Euclidean theory we have been unable (thus far) to transfer to the category of metric spaces and explain what the obstacles seem to be.