The advancements in aberration correctors, pixelated direct electron detectors, and monochromators represent significant milestones in the development of transmission electron microscopy (TEM). These innovations have enabled the imaging of materials' structure, chemistry, and functional properties at the atomic scale. In this talk, I will introduce a novel four-dimensional scanning transmission electron microscopy (4D STEM) method. This method facilitates the imaging of local polarization, electric fields, and charge density in multiferroic oxide nanostructures with sub-angstrom resolution. I will demonstrate how polarization at ferroelectric/insulator interfaces influences functional properties, such as strain, bonding, electric field and charge distributions. Through the combination of 4D STEM and scanning probe microscopy, we have observed unique skyrmion-like polar nanodomains in freestanding PbTiO3/SrTiO3 bilayers transferred onto silicon. These nanodomains can be toggled between states by an applied electric field, leading to substantial alterations in their resistive behaviors. In the subsequent part of the presentation, I will introduce innovative space- and angle-resolved electron energy-loss spectroscopy (EELS) methods. These techniques enable us to uncover novel vibrational modes and emergent phonons at single defects or interfaces in crystalline materials. We can map changes in phonon momentum, revealing the direction of phonon propagation and, consequently, heat flow at the nanoscale. Utilizing this technique, we found that sharp interfaces between different materials exhibit markedly superior heat conduction compared to gradual, diffuse ones. These novel methodologies hold valuable potential for studying real nanodevices and enhancing our comprehension of charge distribution and heat dissipation in nanostructures and interfaces.