All rock masses are seismically anisotropic, but we generally ignore this in our seismic acquisition, processing, and interpretation. The anisotropy nonetheless does affect our data, in ways that limit the effectiveness with which we can use it, as long as we ignore it. This book, produced for use with the fifth SEG/EAGE Distinguished Instructor Short Course, helps us understand why this inconsistency between reality and practice has been so successful in the past and why it will be less successful in the future as we acquire better seismic data (especially including vector seismic data) and correspondingly higher expectations of it. This book helps us understand how we can modify our practice to more fully realize the potential inherent in our data through algorithms which recognize the fact of seismic anisotropy.