Low-frequency (80-240 MHz) radio observations of the solar corona are presented using the Murchison Widefield Array (MWA), and several discoveries are reported. The corona is reviewed, followed by chapters on Type III bursts and circularly-polarized quiescent emission. The second chapter details new Type III burst dynamics. One source component at higher frequencies splits into two at lower frequencies, where the two components rapidly diverge. This is attributed to electron beams traversing a divergent magnetic field configuration, which is supported by extreme ultraviolet jet observations outlining a coronal null point. The third chapter uses Type III burst heights as density probes. Harmonic plasma emission implies ~4x enhancements over background models. This can be explained by electron beams traveling along dense fibers or by propagation effects that elevate apparent source heights. The quiescent corona is compared to model predictions to conclude that propagation effects can largely but not entirely explain the apparent density enhancements. The fourth chapter surveys over 100 spectropolarimetric observing runs. Around 700 compact sources are detected with polarization fractions from less than 0.5% to nearly 100%. They are interpreted as plasma emission noise storm sources down to levels not previously observable. A bullseye structure is reported for coronal holes, where an outer ring surrounds an oppositely-polarized central component that does not match the sign expected of thermal bremsstrahlung. The large-scale polarization structure is shown to be well-correlated with that of a global magnetic field model. The last chapter summarizes results and outlines future work. A preliminary comparison of polarization images to model predictions is shared, along with coronal mass ejection observations revealing a radio arc that is morphologically similar to the white-light structure.