Modern multivariate and time series analyses go beyond the classical normality assumption by modelling data that could combine binary, categorical, extreme and heavy-tailed distributions. Dependence is modeled non-linearly, often in terms of copula functions or stochastic representations. Models for multivariate extremes arise from asymptotic limits. Characterization and modelling of dependence among extremes as well as estimation of probabilities of rare events are topics of on-going research. Advances in high-dimensional multivariate modelling have been achieved by the use of vine pair-copula constructions. Areas of application include biostatistics, psychometrics, genetics, machine learning, econometrics, quantitative risk management in finance and insurance, hydrology and geoscience.