This book provides a comprehensive look at statistical inference from record-breaking data in both parametric and nonparametric settings, including Bayesian inference. A unique feature is that it treats the area of nonparametric function estimation from such data in detail, gathering results on this topic to date in one accessible volume. Previous books on records have focused mainly on the probabilistic behavior of records, prediction of future records, and characterizations of the distributions of record values, addressing some inference methods only briefly. The main purpose of this book is to fill this void on general inference from record values. Statisticians, mathematicians, and engineers will find the book useful as a research reference and in learning about making inferences from record-breaking data. The book can also serve as part of a graduate-level statistics or mathematics course, complementing material on the probabilistic aspects of record values. For a basic understanding of the statistical concepts, a one-year graduate course in mathematical statistics provides sufficient background. For a detailed understanding of the convergence theory of the nonparametric function estimators, a course in measure theory or probability theory at the graduate level is useful. Sneh Gulati is Associate Professor of Statistics at Florida International University in Miami. She is currently an associate editor of the Journal of Statistical Computation and Simulation and has published several articles in statistics. Currently she serves as the president of the South Florida Chapter of the American Statistical Association and is also the chair of the Florida Commission of Hurricane Loss Projection Methodology. William J. Padgett is Professor of Statistics and was the founding Chair of the Department of Statistics at the University of South Carolina, Columbia. He has published numerous papers and articles, as well as three books, on statistics and probability and has served as an associate editor of eight statistical journals, including Technometrics, Lifetime Data Analysis, Naval Research Logistics, Journal of Statistical Computation and Simulation, and the Journal of Statistical Planning and Inference. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics and an elected ordinary member of the International Statistical Institute.