A general and important characteristic of rocks is their elastically nonlinear behavior resulting in significant effects on wave propagation. The nonlinear response of rock is a direct consequence of the compliant nature of rock: the macro-and micro-structure of the material (microcracks, grain-to-grain contacts, etc.). As a result, the material modulus varies as a function of the applied pressure. Interest has grown significantly in the last several years, as illustrated by the increasing number of publications regarding this topic. Here we present a summary of the fundamentals of theory and of experimental observations characteristic of rock, and we address possible applications in geophysics. Two disciplines regarding the nonlinear elasticity of rock have been developed over recent years in tandem: Acoustoelasticity where wave propagation in statically, prestressed materials is studied. Here one relates the variation in applied pressure to the elastic wavespeed in order to extract the nonlinear coefficients. This area of study includes the topic of stress-induced anisotropy. Acoustic nonlinearity where we are interested in the temporary and local variation in the elastic modulus due to the passage of an elastic wave through the material. Wave distortion due to local nonlinear response includes the appearance of wave harmonics and wave-wave interactions that result in sum and difference frequency waves. These effects cannot be explained within the framework of linear acoustics and linear elasticity. Potential applications to seismic petroleum exploration and imaging using conventional tools and methods seem remote at this point. For example, nonlinear wave mixing in order to produce a directed wave at the difference frequency between two waves (termed a Parametric Array in acoustics) has proven to be difficult. We believe this to be especially true at deeper and deeper depths due to the reduction in nonlinear response as a function of overburden. At the same time, we note that wave mixing and the development of other frequencies presents an advantage in detection due to the fact that one can detect waves at controlled frequencies far outside the band of the source wave spectra(um). Furthermore, there is no question that under laboratory or near surface conditions, nonlinear applications show significant promise in the near term. In fact, a surprising aspect of nonlinear research is that, to our knowledge, applications have not been developed in obvious areas such as in civil engineering or in mining applications. Judging from the large number of recent patents applied for, and granted to, the well-logging companies, research in this area will continue to grow.