Because most sedimentary rocks encountered in oil and gas exploration are effectively anisotropic, it is imperative to properly estimate seismic anisotropy and incorporate it into data-processing and imaging algorithms. Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization (SEG Geophysical References Series No. 17) presents a systematic analysis of seismic signatures for azimuthally anisotropic media and describes anisotropic inversion/processing methods for wide-azimuth reflection data and VSP (vertical seismic profiling) surveys. The main focus is on kinematic parameter-estimation techniques operating with P-waves as well as with the combination of PP and PS (mode-converted) data. The part devoted to prestack amplitudes includes azimuthal AVO (amplitude variation with offset) analysis and a concise treatment of attenuation coefficients, which are highly sensitive to the presence of anisotropy. Discussion of fracture characterization is based on modern effective media theories and illustrates both the potential and limitations of seismic methods. Field-data examples highlight the improvements achieved by accounting for anisotropy in seismic processing, imaging, and fracture detection.