The resolution and interpretation of electron microscopy images have historically been limited by electromagnetic lens aberrations and multiple scattering effects. The former problem was addressed through the development of aberration correctors at the turn of the 21st century making sub-Å resolution imaging routinely possible. Solving the multiple-scattering problem took longer but has now been achieved through multislice electron ptychography (MEP), a technique that became practical through developments in detector technology and phase-retrieval algorithms. With spatial resolution now limited only by atomic thermal vibrations, and with the capability for reliable three-dimensional structural reconstruction and light-atom imaging, this technique is a powerful tool for addressing previously intractable material characterization challenges. In this dissertation, I explore the application of MEP for the study of structural distortions that lend functionality to ferroic materials. I will demonstrate how dipoles in polar materials can be quantitatively mapped, leading to the fundamental insight that accurate characterization requires tracking both cationic and anionic species, thereby challenging the validity of approaches based solely on cation-cation displacements. These measurements reveal an unconventional origin of ferroelectricity in strain-engineered sodium niobate thin films and flexoelectricity in strain-gradient-engineered strontium titanate membranes. My study of sodium niobate points to a broader class of ferroelectric perovskites, while my investigation of bent oxide membranes provides new insights that may help resolve long-standing inconsistencies in the understanding of flexoelectricity. With rising interest in the field of moiré engineering with twisted oxide membranes, I also investigate the 3D imaging of stacked heterostructures and show the inadequacy of conventional through-focal imaging for characterization of buried interfaces. While I demonstrate the sensitivity of MEP to detect large interfacial gaps, I emphasize the necessity of cross-sectional imaging to substantiate claims of interlayer coupling, given the limitations imposed by MEP’s nanometer-scale depth resolution. In the last section, I benchmark the performance of the cepstral algorithm for strain mapping applications using pixel array detectors, highlighting the interplay of experimental parameters in optimizing the trade-off between precision and resolution. I discuss the sources of systematic errors in strain measurements and explore how they can be mitigated through modifications in experimental design or analysis workflows.