This paper describes numerical estimation techniques for coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene. The spatial information is modulated by a coded aperture and the spectral information is modulated by a dispersive element. The estimation process decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore an indispensable component of the spectral imager. Numerical estimation results are presented.