The coda of seismic waves consists of that part of the signal after the directly arriving phases. In a finite medium, or in one that is strongly heterogeneous, the coda is dominated by waves which have repeatedly sampled the medium. Small changes in a medium which may have no detectable influence on the first arrivals are amplified by this repeated sampling and may thus be detectable in the coda. We refer to this use of multiple-sampling coda waveforms as coda wave interferometry. We have exploited ultrasonic coda waves to monitor time-varying rock properties in a laboratory environment. We have studied the dependence of velocity on uniaxial stress in Berea sandstone, the temperature dependence of velocity in granite and in aluminum, and the change in velocity due to an increase of water saturation in sandstone. There are many other possible applications of coda wave interferometry in geophysics, including dam and volcano monitoring, time-lapse reservoir characterization, earthquake relocation, and stress monitoring in mining and rock physics.