  These notes present a recent approach to study the high-frequency eigenstates
of the Laplacian on compact Riemannian manifolds of negative sectional
curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of
the semiclassical measures associated with sequences of eigenstates, showing
that high-frequency eigenstates cannot be too localized. The method is extended
to the case of semiclassical Hamiltonian operators for which the classical flow
in some energy range is of Anosov type, and to the case of quantized Anosov
diffeomorphisms on the torus.
