This book, written and edited by over twenty experts in the field, focuses on current and new developments in statistical methods as they relate to causality. It pursues three aims: to provide a compact, state-of-the-art summary of the latest developments in methods for statistical analysis of causality hypotheses; to relate the properties of statistical methods to theories of causality; and to present developments of statistical methods that are novel and have not been published heretofore under one roof. Divided into four accessible and independent parts, each part consists of two or more chapters. In part one counterfactual causality theory is presented and the connection to Bayesian statistical analysis is established. Part two proposes new developments in the domain of methods of analysis of direction dependence. Part three concentrates on propensity score analysis with emphases on matching, inverse weighting, latent covariates, and quasi-experimental designs and causal analysis. The book concludes with presentations on the long-standing tradition of Granger causality and presents new methodologies. Each chapter comes complete with an extensive bibliography. Software discussions are introduced when applicable.