Over the past decade, microseismic monitoring, a technology developed for evaluating completions of wells drilled to produce hydrocarbons from unconventional reservoirs, has grown increasingly popular among oil and gas companies. This book discusses how to process microseismic data, what can and cannot be inferred from such data, and to what level of certainty this might be possible. The narrative of the book follows the passage of seismic waves: from a source triggered by hydraulic fracture stimulation, through hydrocarbon-bearing formations, towards motion sensors. The waves' characteristics encode the location of their source and its focal mechanism. The analysis of various approaches to harvesting the source-related information from microseismic records has singled out the accuracy of the velocity model, fully accounting for the strong elastic anisotropy of hydraulically fractured shales, as the most critical ingredient for obtaining precise source locations and interpretable moment tensors. The ray theory complemented by its modern extensions, paraxial and Fréchet ray tracing, provides the only practical means available today for building such models. The book is written for geophysicists interested in learning and applying advanced microseismic data-processing techniques.