  In this article we survey some of the recent goings-on in the classification
programme of C$^*$-algebras, following the interesting link found between the
Cuntz semigroup and the classical Elliott invariant and the fact that the
Elliott conjecture does not hold at its boldest. We review the construction of
this object both by means of positive elements and via its recent
interpretation using countably generated Hilbert modules (due to Coward,
Elliott and Ivanescu). The passage from one picture to another is presented
with full, concise, proofs. We indicate the potential role of the Cuntz
semigroup in future classification results, particularly for non-simple
algebras.
