Shastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, shastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in shastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and shastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in shastic neurobiological models, a review of mathematical methods for shastic neuronal integrate-and-fire models, shastic partial differential equation models in neurobiology, and shastic modeling of spreading cortical depression.