The knowledge that the propagation of elastic waves can be anisotropic is about 180 years old. At the turn of the 20th century, Rudzki suggested the significance of seismic anisotropy. He studied many of its aspects, but without a real application of his ideas. Research in seismic anisotropy became stagnant after his death in 1916. Beginning at about 1950, the significance of seismic anisotropy for exploration seismics began to be studied, mainly in connection with thinly layered media and the resulting transverse isotropy. But it became clear that the effect of the layer induced anisotropy on the data acquired with the techniques of that time was negligible. In the last two decades of the 20th century, Crampin pointed out that the cracks in a rock mass lead to observable effects from which, in principle, the orientation and the density of the cracks could be determined. Since this information has a direct relevance to the reservoir properties of the rock, the interest in seismic anisotropy was increased considerably. The seismic anisotropy study came into a new era, with more scholars and oil companies focusing their attention on this field. Recent advances in the acquisition technology, the computer technology and the seismic processing technology have allowed the incorporation of anisotropic models into a wide range of seismic methods. In particular, the vertical and tilted transverse isotropies are currently treated as an integral part of the velocity fields employed in pre-stack depth migration algorithms, especially those based on the wave equation. Continued progress in the data-acquisition technology is likely to spur a transition from the transverse isotropy to lower anisotropic symmetries, e.g. orthorhombic ones. With the role of the anisotropy in the seismic exploration in mind, we discuss the origin of anisotropy, P-wave velocity analysis and imaging, processing ,moveout inversion of wide-azimuth data, amplitude-variation-with-offset and AVO analysis and fracture characterization. Today, the anisotropy, as an important part in exploration and reservoir geophysics, has been included in every exploration geophysicist's toolkit.