  We report on recent progress in the program to classify separable amenable
C*-algebras. Our emphasis is on the newly apparent role of regularity
properties such as finite decomposition rank, strict comparison of positive
elements, and Z-stability, and on the importance of the Cuntz semigroup. We
include a brief history of the program's successes since 1989, a more detailed
look at the Villadsen-type algebras which have so dramatically changed the
landscape, and a collection of announcements on the structure and properties of
the Cuntz semigroup.
