The last half century has seen the development of many biological or physical theories that have explicitly or implicitly involved medial descriptions of objects and other spatial entities in our world. Simultaneously, mathematicians have studied the properties of these skeletal descriptions of shape, and, stimulated by the many areas where medial models are useful, computer scientists and engineers have developed numerous algorithms for computing and using these models. The book consists of an introductory chapter, two chapters on the major mathematical results on medial representations, five chapters on algorithms for extracting medial models from boundary or binary image descriptions of objects, and three chapters on applications in image analysis and other areas of study and design. This book will serve the science and engineering communities using medial models and will provide learning material for students entering this field.