The goal of microscopy is to take position-resolved data of things invisible & small and transform that data into something meaningful & macroscopic. In the case of scanning transmission electron microscopy (STEM) we generate position resolved data by raster scanning a focused beam of highly accelerated electrons—also called the probe or the incident beam—on a thin sample and measuring the properties of the electrons that pass through the sample. If we know certain properties of the incident electrons, say their momentum, and then measure that property after having interacted with the sample, we can infer properties about the sample, such as the scattering potential & therefore the locations of the atoms within the sample. We then generate an image where the pixel values represent the measured properties. Obtaining an image that represents the properties of a material lets us understand & convey what is happening in ways that few other forms of science communication can. In this Dissertation, I discuss the concepts behind momentum-resolved STEM (4D-STEM); first with a general presentation of the limiting factors, followed by a more in-depth look at how we refine our measurements and the process by which we transform them into meaningful representations. I show that brightness preservation serves as a better optimization metric than aberration minimization. Finally, I discuss a new physically motivated data transformation that simplifies analysis of 4D-STEM data for high-precision strain measurement & robust grain identification.