This talk is about Kac's inverse problem from 1966: ``Can one hear the shape of a drum?" The question asks whether the frequencies of vibration of a bounded domain determine the shape of the domain. First, we present a quick survey on the known results. Then we discuss the key connection between eigenvalues of the Laplacian and the dynamics of the billiard, which is governed by the so-called ``Poisson Summation Formula''. Finally, we discuss our main theorem that ``one can hear the shape of nearly circular ellipses". This is joint work with Steve Zelditch.