Thermoacoustic tomography (TAT) is an emerging modality of medical imaging which produces high resolution, high contrast tomographic images without exposing patients to dangerous ionizing radiation. In a TAT scan, pulsed radio frequency energy applied to a tissue sample causes rapid thermoelastic expansion and contraction, propagating a pressure wave through the sample. Transducers arranged around the patient's body record this ultrasonic pressure data and there are several reconstruction regimes available to recover a tomographic image from this information. In this talk, I will describe the standard wave equation model for thermoacoustic signal generation and highlight several of the image reconstruction techniques discovered in the past twenty years. I will then present a new Neumann series exact solution due to P. Stefanov and G. Uhlmann. This very elegant method motivates and theoretically justifies wave equation time reversal methods for TAT reconstruction and I will outline some promising numerical algorithms of this type.