In this thesis, the development of computational tools for the analysis of scanning transmission electron microscopy data are presented; these tools are applied to several physical systems, and the resulting insights into the physics and materials science of these systems is detailed; and the fundamental principles of image formation are relayed with an eye towards clarity and accessibility. The first half of the thesis relates to images, image formation, and optimization, first physically and then computationally. Chapter 2 contains an introductory level description of the basic physics of image formation in the electron microscope. The aim is rigor sans mathematical formalism, beginning with a visual approach to the complex integrals of optics and wave propagation. We then turn to an investigation of lenses which stresses the dual real/reciprocal space nature of lens action and information transfer in a microscope, touching briefly on Abbe theory and resolution limits. Finally, the physical basis of the contrast transfer function and optimum focus conditions in the presence of lens aberrations are discussed for weak phase objects, followed by a short description of advanced imaging modes. From physical image formation we turn to computational processing to obtain the best quality images, and Chapter 3 takes up the question of how best to achieve high signal-to-noise ratio images by registration and alignment of image stacks, when low SNRs and high translational symmetry cause a strong propensity toward unit cell misalignments. After demonstrating the subtly specious images that can result from incorrectly aligned data, which can be particularly problematic in low SNR cryoSTEM data, a solution is described whereby all possible pairs of images are aligned, and incorrect alignments are then identified and corrected by enforcing physical consistency in the complete set of alignments. The latter half of the thesis relates to applications in two systems in which structural disorder is an essential element. Chapter 4 focuses on epitaxially bonded quantum dot superlattices. In these materials, the theoretical promise of unprecedented bandstructure control is limited in practice by structural disorder, which localizes the relevant charge carrier states such that a band picture is unsuitable and transport is dominated by thermally activated hopping. Chapter 4 both quantifies in detail and explicates the basic nature of the structural disorder in quantum dot superlattices. Translational as well as orientational disorder are discussed in both the atomic lattice and superlattice, a connection is established between the disorder across many orders of magnitude of length, and the implications for electronic structure and growth are addressed. Chapter 5 examines charge density wave materials, in which the lattice positions and charge distribution of a crystal are modulated with some periodicity larger than the unit cell. A method for locally mapping fields of periodic lattice displacements at each atomic site is developed, and applied to a charge ordered manganese oxide to reveal picometer scale, transverse displacements fields of the lattice. Nanoscale spatial heterogeneity in two orthogonal modulations is revealed, and competition between the two fields is suggested by their local spatial anti-correlation and the detailed structure of their defects. Conclusions are in Chapter 6.