This book gives a detailed account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. A section is devoted to statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field. The book considers recent developments on weak dependent time series, including some new results for Markov chains, and fills a gap between the probability and statistical literature and the dynamical system literature. The book also presents new results on strong dependence with an emphasis on non-linear processes and random fields.