This book provides a broad introduction to the fascinating subject of environmental space-time processes; addressing the role of uncertainty. Within that context, it covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment. The contents reflect the authors' cumulative knowledge gained over many years of consulting and research collaboration. In particular, with members of their research group, they developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes. Furthermore they indicate new directions for development. This book contains technical and non-technical material and it is written for statistical scientists as well as consultants, subject area researchers and students in related fields.