Inverse spectral problems ask how much geometric information is encoded in spectral data. For example, Mark Kac´s question ``Can you hear the shape of a drum?´´ asks whether a plane domain, viewed as a vibrating membrane, is determined by the Dirichlet eigenvalue spectrum of the associated Laplacian, equivalently, by the characteristic frequencies of vibration. The lecture will focus on Kac´s question and its generalization to Riemannian manifolds. We will give a partial survey of both positive and negative results and techniques.