Spectral imaging, the simultaneous imaging and spectroscopy of a radiating scene, is a fundamental sensing technique with pervasive applications in the physical and life sciences. Nevertheless, inherent limitations exist on the attainable temporal, spatial, and spectral resolutions in conventional spectral imaging techniques that rely solely on physical measurement systems such as two-dimensional detectors which are incapable of capturing intrinsic three-dimensional data. In this presentation, research toward the development of a class of novel spectral imaging techniques that overcome the limitations of conventional methods is described. The approach is based on distributing the spectral imaging task between a physical and a computational system and then digitally forming spectral images of interest from multiplexed measurements by means of solving an inverse problem. The development involves the following steps: First, a novel optical system is proposed with the goal of overcoming the resolution limitations of conventional systems. Second, the associated inverse problem for image reconstruction is formulated by combining multiplexed measurements with an image formation model based on an estimation-theoretic framework. Third, computationally efficient algorithms are designed to solve the resultant nonlinear optimization problems. Since an inversion is required for the reconstruction of the spectral imaging information from incomplete and imperfect measurements, a rigorous theory is essential for quantitative characterization of the performance of the techniques. Therefore, in addition to the development of each technique, we aim to obtain fundamental performance bounds in order to characterize the estimation uncertainties and quantify performance limits, as well as to attain insights that would guide optimal system design. Finally, we illustrate the effectiveness of the proposed computational spectral imaging techniques in applications involving remote sensing of space plasmas.