The Rokhlin property for actions of compact groups on C*-algebras was introduced by Ilan Hirshberg and Wilhelm Winter, and is a noncommutative analog of freeness for actions on compact spaces. The definition for finite group actions has been around for much longer, and finite group actions with the Rokhlin property are more or less well understood by now. On the other hand, very little is known about the Rokhlin property for compact, non-finite, group actions. This talk will focus on the Rokhlin property for circle actions. We will introduce the definition, present basic properties and construct some examples. We will show that Kirchberg algebras are preserved under formation of crossed products by such actions. The main result of the talk is that circle actions with the Rokhlin property on Kirchberg algebras are classified up to conjugacy by their equivariant K-theory. We will then specialize to circle actions on the Cuntz algebra \mathcal{O}_2. In this case, it will be shown that circle actions with the Rokhlin property are generic, that any two of them are conjugate, and that the restriction to any finite subgroup of the circle again has the Rokhlin property (in general they have Rokhlin dimension one).