Pinwheels are certain singular Lagrangians in four-dimensional symplectic manifolds. In this talk, we focus on the case of the complex projective plane, where pinwheels arise naturally as visible Lagrangians in its almost toric fibrations or, alternatively, as vanishing cycles of a certain class of degenerations. Pinwheels have been shown to have interesting rigidity properties in pioneering work by Evans--Smith. The goal of this talk is to discuss yet another rigidity feature, namely that pinwheels are Lagrangian barriers in the sense of Biran. This means that their complement has strictly smaller Gromov width than the ambient space. This is joint work with Felix Schlenk.