Pureness is a regularity property that plays a prominent role in the structure of C*-algebras. It can be thought of the $\mathcal{Z}$-stability at the level of the Cuntz semigroup of the algebra and at the same time is proved to be equivalent to certain weak comparison and divisibility properties. This characterization implies that every simple, non-elementary C*-algebra with a unique quasitrace and mild comparison has strict comparison. The characterization is also used to show that the class of pure C*-algebras behaves well under extensions. Further, for a separable C*-algebra $A$, one has that $\mathcal{Z}$-stability is equivalent to demanding that the uncorrected central sequence algebra of $A$ is pure, which in turn is equivalent to saying that said algebra is almost divisible. This is joint work with Ramon Antoine, Hannes Thiel, and Eduard Vilalta; and with Hannes Thiel and Eduard Vilalta.