A C*-algebra is called pure if it has good comparison and divisibility properties; more precisely, its Cuntz semigroup is almost unperforated and almost divisible. A natural question, raised at several conferences, is whether the minimal tensor product $A \otimes B$ remains pure whenever $A$ is. In this talk, we shall see results addressing this question when $B = C(X)$. We will also discuss applications to crossed products. This talk is based on two joint works: one with Vilalta, and another with Archey, Buck, Mohammadkarimi, and Phillips.