Joint work with Ivan Smith. Let p be a positive integer. Take the quotient of a 2-disc by the equivalence relation which identifies two boundary points if the boundary arc connecting them subtends an angle which is an integer multiple of (2 pi / p). We call the resulting cell complex a 'p-pinwheel'. We will discuss constraints on Lagrangian embeddings of pinwheels. In particular, we will see that a p-pinwheel admits a Lagrangian embedding in CP^2 if and only if p is a Markov number. Time permitting, I will discuss nondisplaceability results, which are a purely symplectic analogue of the Hacking-Prokhorov classification of Q-Gorenstein degenerations of CP^2.