Phase transformations in mantle mineralogies probably cause the transition zone seismic discontinuities, nominally at 410, 520, and 660 km depth. Thermodynamic principles govern phase transformations, making them sensitive to changes in the mantle's ambient conditions through the thermodynamic response: Changes in temperature or composition shift the transformation to a different pressure, creating topography on a level discontinuity. With this use as an exploratory tool for the mantle in mind, we review the basic seismological and phase equilibrium concepts underlying the detection and interpretation of the seismic wave arrivals associated with the transition zone discontinuities. Reviewing the evidence for and against the phase transition model, we conclude that it is viable and describe how discontinuities have been and can be used to probe the physical and chemical state of the transition zone. ¿ 2000 American Geophysical Union