Very detailed information about the atomic and electronic structure of materials can be obtained via atomic-scale resolution scanning transmission electron microscopy (STEM). These experiments reach the limits of current microscopes, which means that optimal experimental design is a key ingredient in success. The step following experiment, extraction of information from experimental data is also complex. Comprehension of experimental data depends on comparison with simulated data and on fundamental understanding of aspects of scattering behavior. The research projects discussed in this thesis are formulated within three large concepts.1. Usage of simulation to suggest experimental technique for observation of a particular structural feature. Two specific structural features are explored. One is the characterization of a substitutional dopant atom in a crystal. Annular dark field scanning transmission electron microscope (ADF-STEM) images allow detection of individual dopant atoms in a crystal based on contrast between intensities of doped and non-doped column in the image. The magnitude of the said contrast is heavily influenced by specimen and microscope parameters. Analysis of multislice-based simulations of ADF-STEM images of crystals doped with one substitutional dopant atom for a wide range of crystal thicknesses, types and locations of dopant atom inside the crystal, and crystals with different atoms revealed trends and non-intuitive behaviors in visibility of the dopant atom. The results provide practical guidelines for the optimal experimental setup regarding both the microscope and specimen conditions in order to characterize the presence and location of a dopant atom. Furthermore, the simulations help in recognizing the cases where detecting a single dopant atom via ADF-STEM imaging is not possible. The second is a more specific case of detecting intrinsic twist in MoS2 nanotubes. Objective molecular dynamics simulations coupled with a density functional-based tight-binding model revealed that a stress-free single-walled (14,6) MoS2 nanotube has a torsional deformation of 0.87 °/nm. Comparison between simulated electron diffraction patterns and atomic-resolution ADF-STEM images of nanotubes with and without the small twist suggested that these experimental techniques are viable routes for detecting presence of the torsional deformation. 2. Development of theory to cast light on aspects of scattering behavior that affect STEM data. STEM probe intensity oscillates as the probe transmits through a crystalline sample. The oscillatory behavior of the probe is extremely similar during transmission through 3-D crystals and the hypothetical structure of an isolated column of atoms, a 1-D crystal. This indicates that the physical origin of oscillation in intensity is not due to scattering of electrons away from one atomic column and subsequent scattering back from neighboring columns. It leaves in question what the physical origin or intensity oscillation is. This question was answered here by analysis of electron beam behavior in isolated atomic columns, examined via multislice-based simulations. Two physical origins, changes in angular distribution of the probe and phase shift between the angular components, were shown to cause oscillation in beam intensity. Sensitivity of frequency of oscillation to different probe and sample parameters was used to better understand the influence of the two physical origins on probe oscillation. 3. Acquisition of atomic-scale STEM data to answer specific questions about a material. Graphene, due to its 2-Dimensionality, and due to its thermal, optical, electrical, and mechanical properties, which are conducive to providing a unique material for incorporation in devices, has gained a lot of interest in the research world and even spurred start-ups. There are several feasible routes of graphene synthesis, among which chemical exfoliation of graphite is a promising method for mass-scale, low-cost production of graphene. Chemical exfoliation of graphite to produce graphene is a two-step process: oxidation to exfoliate the graphite layers, which results in graphene oxide, and reduction of graphene oxide, to produce graphene as a final product. Here, we examined the atomic and electronic structure of graphene oxide and of the reduced sheets. Two different methods of reduction, thermal reduction in vacuum and aqueous reduction in atmosphere, were compared. TEM-based techniques were used for nanoscale characterization. GO was synthesized using the modified Hummer's method and presence of single layer sheets was confirmed by electron diffraction (ED). Non-uniform distribution of oxygen in GO was observed using Z-contrast imaging in STEM. Presence of sp2 and sp3 hybridized carbon bonds in GO was confirmed by examining the fine structure of carbon K-edge in electron energy loss spectra (EELS). Changes in oxygen distribution and electronic structure of carbon were monitored using the same techniques in situ during thermal reduction of GO to graphene. Change in oxygen level and carbon hybridization was gradual with increasing temperature, with complete conversion to oxygen-absent, sp2 hybridized carbon sheet at 1000 ̊C. Gradual change confirmed the ability to fine-tune the level of oxygen on carbon sheets using thermal reduction in vacuum. Instantaneous heating from room temperature to 1000 ̊C showed formation of holes in the graphene product. A several-hour gradual heating process was suggested to decrease perforation in graphene sheets. The second reduction process, aqueous thermal reduction in ambient pressure, did not lead to completely sp2 hybridized carbon sheets, observed using EELS. Presence of oxygen was also observed via x-ray photoemission spectra (XPS). Yet, electrical resistance of the product was 5 orders of magnitude less than the starting GO sheets. This property was explained by examining the atomic structure of the reduced GO. High resolution conventional TEM (CTEM) images of nano-scale section of the reduced GO showed randomly shaped crystalline areas and amorphous areas, with crystalline area being above the 2-D percolation threshold and thus explaining the conductive property.