When attempting to discretize the Fourier transform (or STFT), lattices are the clear first choice. They have a duality theory that culminates in the Poisson summation formula and support an elegant theory of periodic functions. Thus when trying to extend sampling results to non-uniform point sets, it is natural to try to preserve as many of these properties of lattices as is possible. Quasicrystals (also called cut and project sets) were developed for precisely this purpose. They also have a natural duality theory culminating in a version of the Poisson summation formula, and they support a theory of almost-periodic functions. I will discuss some of these properties, along with recent results of Meyer about sampling on quasicrystals.