Highly localized structural and spectroscopic measurements using scanning transmission electron microscopy (STEM) enable the exploration of atomic displacements in systems with nanoscale heterogeneity across a wide variety of materials. Further, they allow for the investigation of connections between charge, spin, lattice, and orbital degrees of freedom. These insights can have significant implications for materials design and performance. In this work, precise atomic position measurements are used in combination with diffraction and spectroscopy-based STEM modalities to investigate atomic displacements in materials from quantum dots to thin films and bulk crystals.First, strain defects in epitaxially connected quantum dot superlattices are elucidated using a newly developed strain mapping technique. These measurements reveal distinct defect types present in inter-dot connections. The strain defects are then tracked as they evolve during in situ annealing in the STEM, providing insights into the relative energetics of the strain defects and suggesting design rules for improving the processing and final electronic properties of the superlattices. The precise measurement of atomic column positions by atom tracking in high-angle annular dark-field (HAADF)-STEM imaging is becoming more common due to the availability and effectiveness of aberration correction. This technique holds enormous potential with respect to the study of the physics underlying quantum phenomena. However, the strong channeling behavior of the STEM probe as it propagates along atomic columns can lead to unexpected contrast that influences atomic position measurements. One of these effects, produced by coherently displaced anions in shared cation-anion columns, is shown experimentally to cause measured cation positions to appear displaced by several picometers from their true positions. The origins of this effect and its dependence on experimental parameters are examined through multislice simulations, and strategies for avoiding or minimizing the effect are discussed. Oxygen deficient LaNiO3 ? _ is presented as a case study for quantifying atomic displacements in a sample containing coherently displaced anions with the potential to induce anomalous atomic position measurements. First, vacancy-ordered oxygen deficient domains are mapped in a bulk crystal using 4D-STEM. The displacement patterns associated with two distinct vacancy ordered phases are then extracted through careful Fourier analysis, confirming a previously reported structure model for one phase and identifying the lattice distortions in the second phase for the first time. Finally, a new Jahn-Teller distorted infinite-layer structure is discussed for which careful atomic position measurements were instrumental in determining the structure. Here, the low sample volume and large available phase space prevented a traditional structure refinement by x-ray scattering. Instead, HAADF- and annular bright-field (ABF)-STEM imaging of multiple zone axes were used to first reduce the phase space for an x-ray refinement and then to deduce the true structure from multiple possible refinements. These measurements reveal a complex and highly distorted structure dictated by competition between the two-dimensional Jahn-Teller effect and geometric frustration induced by coupling between atomic layers. Electron energy loss spectroscopy is used to further probe the electronic structure of the material.