This book addresses copula approaches to competing risks models for dependent latent failure times. It will establish the fundamentals of dependent competing risks models, as well as a range of recent developments to identifiability and estimation using copulas. Readers will learn from the presentation of theory in relation to its applications in different subject areas in economics, engineering, and medicine. The comprehensive knowledge provided in this book gives readers an overview of existing models for dependent competing risks, which are not found in other volumes. The book covers basic statistical ideas, such as “parametric latent failure time models”, theoretical issues, such as “identifiability of the competing risks model”, and model comparisons, such as comparative studies for “different copulas and different models for hazard functions”. Aside from the introductory materials, the authors cover new and recently developed methodologies. The new solutions address the identifiability problems in competing risks models that rely on copula modelling. Copula models and other competing risks models are presented in a unified theoretical framework and illustrated with data from various disciplines (such as economics, engineering, and medicine). The book also includes applications with real data and the code (written by R and/or Stata) will be made available for easy practice purposes. A selection of exercises and their solutions will be available online. This book serves as a good reading for senior undergraduates and postgraduate students studying in such courses as “Multivariate Survival Analysis”, “Survival Data Analysis” or “Advanced Econometrics”. This book would also serve as a useful reference for empirical researchers in a wide range of disciplines.