The cross-entropy (CE) method is one of the most significant developments in randomized optimization and simulation in recent years. This book explains in detail how and why the CE method works. The simplicity and versatility of the method is illustrated via a diverse collection of optimization and estimation problems. The book is aimed at a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist and practitioner, who is interested in smart simulation, fast optimization, learning algorithms, and image processing.