Understanding change is essential in most scientific fields. This is highlighted by the importance of issues such as shifts in public health and changes in public opinion regarding politicians and policies. Nevertheless, our measurements of the world around us are often imperfect. For example, measurements of attitudes might be biased by social desirability, while estimates of health may be marred by low sensitivity and specificity. In this book we tackle the important issue of how to understand and estimate change in the context of data that are imperfect and exhibit measurement error. The book brings together the latest advances in the area of estimating change in the presence of measurement error from a number of different fields, such as survey methodology, sociology, psychology, statistics, and health. Furthermore, it covers the entire process, from the best ways of collecting longitudinal data, to statistical models to estimate change under uncertainty, to examples of researchers applying these methods in the real world. The book introduces the reader to essential issues of longitudinal data collection such as memory effects, panel conditioning (or mere measurement effects), the use of administrative data, and the collection of multi-mode longitudinal data. It also introduces the reader to some of the most important models used in this area, including quasi-simplex models, latent growth models, latent Markov chains, and equivalence/DIF testing. Further, it discusses the use of vignettes in the context of longitudinal data and estimation methods for multilevel models of change in the presence of measurement error.