This research presents advances in time-synchronized phasor (i.e.,synchrophasor) estimation and imaging with very-low-frequency electric fields. Phasor measurement units measure and track dynamic systems, often power systems, using synchrophasor estimation algorithms. Two improvements to subspace-based synchrophasor estimation algorithms are shown. The first improvement is a dynamic thresholding method for accurately determining the signal subspace when using the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. This improvement facilitates accurate ESPRIT-based frequency estimates of both the nominal system frequency and the frequencies of interfering signals such as harmonics or out-of-band interference signals. Proper frequency estimation of all signals present in measurement data allows for accurate least squares estimates of synchrophasors for the nominal system frequency. By including the effects of clutter signals in the synchrophasor estimate, interference from clutter signals can be excluded. The result is near-flat estimation error during nominal system frequency changes, the presence of harmonic distortion, and out-of-band interference. The second improvement reduces the computational burden of the ESPRIT frequency estimation step by showing that an optimized Eigenvalue decomposition of the measurement data can be used instead of a singular value decomposition. This research also explores a deep-learning-based inversion method for imaging objects with a uniform electric field and a 2D planar D-dot array. Using electric fields as an illumination source has seen multiple applications ranging from medical imaging to mineral deposit detection. It is shown that a planar D-dot array and deep neural network can reconstruct the electrical properties of randomized objects. A 16000-sample dataset of objects comprised of a three-by-three grid of randomized dielectric constants was generated to train a deep neural network for predicting these dielectric constants from measured field distortions. Increasingly complex imaging environments are simulated, ranging from objects in free space to objects placed in a physical cage designed to produce uniform electric fields. Finally, this research relaxes the uniform electric field constraint, showing that the volume of an opaque container can be imaged with a copper tube antenna and a 1x4 array of D-dot sensors. Real world experimental results show that it is possible to image buckets of water (targets) within a plastic shed These experiments explore the detectability of targets as a function of target placement within the shed.