  We give a number of new characterizations of the Jiang-Su algebra Z, both
intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and
K-theoretic conditions. Along the way we study divisibility properties of
C*-algebras, we give a precise characterization of those unital C*-algebras of
stable rank one that admit a unital embedding of the dimension-drop C*-algebra
Z_{n,n+1}, and we prove a cancellation theorem for the Cuntz semigroup of
C*-algebras of stable rank one.
