  In a celebrated paper '"Can one hear the shape of a drum?"' M. Kac [Amer.
Math. Monthly 73, 1 (1966)] asked his famous question about the existence of
nonisometric billiards having the same spectrum of the Laplacian. This question
was eventually answered positively in 1992 by the construction of noncongruent
planar isospectral pairs. This review highlights mathematical and physical
aspects of isospectrality.
