  Tame abstract elementary classes are a broad nonelementary framework for
model theory that encompasses several examples of interest. In recent years,
progress toward developing a classification theory for them have been made.
Abstract independence relations such as Shelah's good frames have been found to
be key objects. Several new categoricity transfers have been obtained. We
survey these developments using the following result (due to the second author)
as our guiding thread:
  $\mathbf{Theorem}$
  If a universal class is categorical in cardinals of arbitrarily high
cofinality, then it is categorical on a tail of cardinals.
