Downhole microseismic monitoring of stimulation and production of unconventional reservoirs has resulted in renewed industry interest in seismic anisotropy. This occurred not only because anisotropy of hydrocarbon-bearing shales is among the strongest in rocks but also because downhole microseismics shifts the focus from the standard exploration of P-waves to shear waves. The consequences of the difference in wave type are profound for geophysicists because everyone involved – from theoreticians to developers and users of microseismic data-processing software – must be aware of shear-wave splitting, singularities, and multivalued wavefronts, which have been largely irrelevant for P-waves propagating in relatively simple geologic settings. Anisotropy and Microseismics leads readers on a path of discovery of rarely examined wave phenomena and their possible usage. Most of the chapters begin by formulating a question, followed by explanations of what is exciting about it, where the mystery might lie, and what could be the potential value of answering the question. Importantly, the findings entail useful applications, as showcased by the unmistakably practical flavor of the chapters on microseismic event location, moment tensor inversion, and imaging. As an investigation of microseismic methodologies and techniques is conducted, it often yields unexpected results.