Computed tomography (CT) has grown into a major workhorse in radiology since its emergence in the 1970's, for its noninvasiveness, three-dimensional information, and superior contrast resolution. There had been a number of major advances in the CT technology, including optimization-based reconstruction methods, which can be designed to reduce image artifacts and enable flexible scanning configuration design. More recently, there has been a renewed interest in exploring the energy information in CT imaging using multispectral scans. A number of commercial scanners are available to acquire dual-energy scan data for a range of clinical applications. On the other hand, a common limitation shared by almost all commercial dual-energy CT scanners is the significant addition of special hardware to conventional diagnostic CT, adding on to the already-expensive cost of CT systems. Part of the reason for the dependence on the special hardware to acquire dual-energy or multispectral CT data is the need to conform to the data conditions required by the reconstruction methods that include either data-domain or image-domain decomposition and the failure to take advantage of the design flexibility enabled by fully-modeled, optimization-based reconstruction methods, such as the one-step inversion methods for multispectral CT. In this dissertation work, we aim to propose a one-step, optimization-based reconstruction method and enable novel, non-standard scan configurations of potential practical significance for multispectral CT that can be readily implemented on existing conventional CT scanners with no or minimum system modification. We start with the development of the method, including a non-linear data model, a non-convex optimization program, and an algorithm for numerically solving the program, and applied the method to both simulated and real data collected from standard, full-scan and non-standard, partial-scan configurations. The results suggest that fast, low-dose, and low-cost multispectral CT can be enabled by the proposed optimization-based reconstruction and the ASD-NC-POCS algorithm.