Basic models for the achievable x-ray system detection efficiency and spatial resolution are reviewed and applied to the design and construction of a modular x-ray computed tomography (CT) system composed of a commercially available microfocus x-ray source and a modular optically-coupled-CCD-scintillator x-ray detector. New approaches are taken to model the detector's interaction with the polychromatic x-ray source. Models governing x-ray source and x-ray detector resolution were used to design the system for a range of system performance goals, most generally, one micrometer spatial resolution with maximized detection efficiency. Measurements of the system's detection count rates under varying conditions were compared with those predicted by the polychromatic x-ray beam spectra model and the modeled energy-dependence of the x-ray detector's detection efficiency. The spatial resolution of the x-ray detector's optical design is analyzed, and discussed in the light of x-ray detector resolution modeling. With precautions taken at the sample rotation stage for experimental accommodations (load capacity and positioning), the unique modularity of the complete μXCT (micrometer-resolved x-ray computed tomography) system is ideal for performing in situ experimentation in a lab-scale setting. With exception of synchrotron beamline researchers who have unrivaled access to highly demanded synchrotron μXCT facilities, the lab-scale setting is ideal for the performing frequent or long term 4D sample characterization. The 4D characterization capabilities of the instrument are demonstrated on two solder systems using in situ μXCT. A near-eutectic 63Sn-37Pb butt-joint was studied with the goal of quantifying three dimensional (3D) microstructural constituents, and tracking the microstructure in four dimensions using in situ μXCT imaging amongst an applied tensile load to quantify local plastic strain as a function of microstructure and global strain. The 3D character of lead-rich dendrites resulting from non-equilibrium solidification was revealed, and the 4D dataset is discussed. The imaging capabilities of the system are also demonstrated on a Sn-0.7Cu solder system undergoing failure from electromigration at 100°C and 104A/cm2. The migrating species, copper and tin, were observable through substrate dissolution, solder buildup, and the formation of reaction products in the solder joint.