The development of fast pixelated direct electron detectors allows the collection of full scattering information at every scanning point in Scanning Transmission Electron Microscopy (STEM). With two scanning directions (x, y) and two momentum dimensions (kx, ky), this results in a four-dimensional dataset, thus the technique is colloquially referred to as 4D-STEM. 4D diffraction data is not readily interpretable, so it must be processed into a more interpretable two-dimensional image. While traditional imaging modes like high-angle angular dark field and bright field images can be replicated, new methods of processing the diffraction data like Center-of-Mass (COM) imaging can quantitatively measure electric field or other properties of the sample. Thus, a better understanding of what information is stored and where in the diffraction pattern will better inform how we can extract quantitative information from the 4D diffraction dataset. In the first part of this thesis, I go over theoretical calculations for diffraction patterns for a variety of samples. By demonstrating how contrast and movement of the bright disk is affected by sample size compared to probe size, I show how the virtual detector geometry of COM imaging affects what length-scale of electromagnetic field is being measured rather than electric versus magnetic fields. Simulations of multiple scattering demonstrate the signal-to-noise efficiency of second moment imaging for thicker biological samples. Finally, a theoretical calculation of polarity contribution in nanobeam electron diffraction (NBED) from 2D materials makes explicit the origin and Z-dependence of the violation of Friedel’s Law even in monolayer samples. In the second part of my thesis, I go over new imaging modes. By understanding how tilt affects placement of diffracted disks in a 2D material, I quantitatively map the in-plane rotation, out-of-plane tilt, and strain in a corrugated sheet of MoS2. Finally, I show how supervised machine learning can be used for high-resolution phase retrieval as a faster, more transferable process than ptychography to demonstrate its capability as a powerful tool for guiding further 4D-STEM characterization development.