This book explores event-based estimation problems. It shows how several stochastic approaches are developed to maintain estimation performance when sensors perform their updates at slower rates only when needed. The self- contained presentation makes this book suitable for readers with no more than a basic knowledge of probability analysis, matrix algebra and linear systems. The introduction and literature review provide information, while the main content deals with estimation problems from four distinct angles in a stochastic setting, using numerous illustrative examples and comparisons. The text elucidates both theoretical developments and their applications, and is rounded out by a review of open problems. This book is a