This survey provides a comprehensive overview of cross-validation (CV) procedures for model selection, aiming to relate empirical results to recent advances in model selection theory. It discusses the theoretical and practical aspects of CV, including its simplicity and universality, while highlighting areas where CV may fail. The survey covers various model selection procedures, such as penalization, unbiased risk estimation, and structural risk minimization, and provides guidelines for choosing the best CV procedure based on the specific problem at hand. Key topics include the statistical framework, model selection paradigms, different types of CV procedures, their statistical properties, and their performance in various frameworks. The survey also addresses specificities in density estimation, robustness to outliers, time series, and large numbers of models, as well as algorithmic complexity and future research directions.This survey provides a comprehensive overview of cross-validation (CV) procedures for model selection, aiming to relate empirical results to recent advances in model selection theory. It discusses the theoretical and practical aspects of CV, including its simplicity and universality, while highlighting areas where CV may fail. The survey covers various model selection procedures, such as penalization, unbiased risk estimation, and structural risk minimization, and provides guidelines for choosing the best CV procedure based on the specific problem at hand. Key topics include the statistical framework, model selection paradigms, different types of CV procedures, their statistical properties, and their performance in various frameworks. The survey also addresses specificities in density estimation, robustness to outliers, time series, and large numbers of models, as well as algorithmic complexity and future research directions.