A correlation matrix is a positive semidefinite matrix with ones on its diagonal, and the set of all such matrices of a given size is called the elliptope. When one draws a correlation matrix uniformly at random from this convex body in high dimensions, the eigenvalues form a random point cloud. The open problem is to determine whether this empirical spectral distribution converges weakly to a deterministic limit as dimension grows, and if so, to characterize that limiting measure explicitly in terms of a density or moment sequence.