There is a close relation between the eigenvalues of the Laplace-Beltrami operator of a Riemannian manifold and the set of lengths of its closed geodesics. Moreover, from these spectra one can extract additional geometric properties of the manifolds. In my talk I will describe some new and old results of this type. In particular, I will discuss the question of how much information can be obtained when we have only partial information on the spectrum.