Knowledge of the spatial distribution and evolution of embedded charge in thin dielectric materials has important applications in semiconductor, high-power electronic device, high-voltage DC power cable insulation, high-energy and plasma physics apparatus, and spacecraft industries. Knowing how, where, and how much charge accumulates and how it redistributes and dissipates can predict destructive charging effects. Pulsed Electro-acoustic (PEA) measurements— and two closely related methods, Pressure Wave Propagation (PWP) and Laser Intensity Modulation (LIMM)— nondestructively probe such internal charge distributions. We review the instrumentation, methods, theory and signal processing of simple PEA experiments, as well as the related PPW and LIMM methods. We emphasize system improvements required to achieve high spatial resolution for in vacuo measurements of thin dielectrics charged using electron beam injection.