In this talk, I will discuss the interplay between the geometry of Riemannian manifolds and properties of eigenfunctions and eigenvalues of the Laplacian. Of particular interest is the relationship between the chaotic behavior of the manifold, in terms of ergodic geodesic flow, and chaotic behaviour of eigenfunctions. Connections will be made between eigenfunctions of the Laplacian and number theory via the theory of modular forms.