Spectral computed tomography (CT) refers to a variety of imaging techniques, whereby projection data are recorded at multiple energies. This extra spectral information can be leveraged to classify and quantify materials based on their chemical properties and may improve dose efficiency for many clinical protocols. A number of potential applications have been demonstrated and FDA approved; however, widespread clinical adoption has not yet been achieved. We believe that this is due, in part, to the fact that current spectral CT systems are not achieving their full potential, which requires refinement to every step of the image formation process. In this work we propose several potential improvements to different parts of the spectral CT imaging chain, including data acquisition, pre-processing, and image reconstruction. The broad goal is to improve dose efficiency and overall image quality. The proposed methods are applicable to any spectral CT system, including commercially available dual-energy scanners as well as multi-energy photon-counting systems, which are being actively researched. First, we consider a task-based framework that can be used to determine optimal acquisition parameters and to guide hardware design. The proposed metric provides a mechanism for quantifying and predicting the relationship between imaging parameters and material classification performance. Our simulation studies support the fact that this rapidly computable metric accurately predicts optimal system configurations. After the projection data are acquired, an important prereconstruction step called ``basis-material decomposition" is performed. We present a projection-space basis-material decomposition method that makes near-optimal use of the spectral information, while requiring only a few iterations. This should make it possible to compute accurate basis-material sinograms in clinically reasonable amounts of time. Lastly, spectral CT involves reconstructing multiple data channels, which could correspond to different energies or basis materials. Since these channels all represent the same basic anatomy, there are likely to be strong inter-channel correlations and shared edges. We propose a technique for jointly reconstructing multi-channel images by generalizing the popular total variation (TV) penalty to vector functions. Our results indicate that this approach has benefits over sequentially processing each energy channel, which is how commercially available dual-energy scanners work, today. We believe the developed techniques may also be applicable to problems outside of CT, such as PET/MRI and other situations that involve reconstructing multiple images with shared anatomical features.