Limit theorems have played a fundamental role in the development of the theory and practice of probability and statistics. Over the last fifty years many important developments have taken place, one of these being the so-called 'Hungarian construction' for proving strong and weak approximations (invariance principles) for various processes. Significant advances since have made this 'construction school' quite international due to the highly important contributions made by mathematicians worldwide. This book presents an account of this methodology which is both timely and up to date. Particular emphasis is given to renewal and related processes, weighted approximations of empirical and quantile processes, as well as the asymptotic distributions of functionals of these weighted processes. This volume will appeal to graduates and researchers in probability and mathematical statistics.