  This is a survey of recent results on quantum ergodicity, specifically on the
large energy limits of matrix elements relative to eigenfunctions of the
Laplacian. It is mainly devoted to QUE (quantum unique ergodicity) results,
i.e. results on the possible existence of a sparse subsequence of
eigenfunctions with anomalous concentration. We cover the lower bounds on
entropies of quantum limit measures due to Anantharaman, Nonnenmacher, and
Rivi\`ere on compact Riemannian manifolds with Anosov flow. These lower bounds
give new constraints on the possible quantum limits. We also cover the non-QUE
result of Hassell in the case of the Bunimovich stadium. We include some
discussion of Hecke eigenfunctions and recent results of Soundararajan
completing Lindenstrauss' QUE result, in the context of matrix elements for
Fourier integral operators. Finally, in answer to the potential question `why
study matrix elements' it presents an application of the author to the geometry
of nodal sets.
