Recently introduced Sparse-Spectrum (SS) model for random processes and fields is based on the trigonometric series with discrete random spectral support and random amplitudes. SS model offers a simple and computationally effective presentation for wide band random fields and processes. SS fields are non-Gaussian and have richer statistics than Gaussian fields with the same power spectrum. We present the general concept of the Sparse Spectrum and discuss its applications for the modeling of the surface waves and phase perturbations of the optical waves propagating through atmospheric turbulence. We address the issue of the sparsity metrics and present the experimental evidence of the spectral sparsity found in the surface elevation data.