The subsurface of the Earth consists typically of media that are not homogeneous, but rather heterogeneous (or inhomogeneous), such as sequences of homogeneous layers where each layer has a different density and wave velocity, or zones where the wave velocity and medium parameters vary smoothly with position. This chapter looks at the theory of how seismic waves propagate in such heterogeneous media. In addition, coverage includes applications of the theory to well surveys and logs (tools used in exploration seismology), the Wiechert–Herglotz method for computing how the seismic wave velocity varies with position from measurements of seismic wave travel times, the eikonal equation (an equation for computing wave travel times), zero-offset ray tracing (a relatively simple technique for roughly estimating the nature of the seismic data that might be recorded in regions of complex subsurface structure), diffracted seismic waves, acoustic waves in heterogeneous materials, and ray equations (for computing the paths of seismic waves in heterogeneous media).