The Weil representation, in its simplest form, is a remarkable group of automorphisms acting on L^2(R)  (in this form, it is not due to Weil).  I will introduce it and explain how it arises naturally in mathematics and physics.  I will use it to indicate another approach to the interpolation theorem of Radchenko--Viazovska, which asserts that an even Schwartz function on the real line is uniquely determined by  its values, and the values of its Fourier transform, at the square roots of integers. This is joint work with Mathilde Gerbelli-Gauthier.