The Vector AutoRegressive (VAR) Model is a popular model for the analysis of a multivariate time series. It allows to investigate the impact changes in one time series have on other ones. A drawback of the VAR is the risk of overparametrization because the number of parameters increases quadratically with the number of included time series. This undermines the ability to identify important relationships in the data and to make accurate forecasts. In high dimensions, we therefore use sparse estimation. The approach is sparse in the sense that some of the parameters are estimated as exactly zero, thereby easing interpretation. A network analysis follows from the sparse estimation, and visualizes the dependencies. We present several applications, and show the forecast performance. We briefly discuss our recent work on t-distributed error terms, inclusion of cointegration equation, multi-class estimation, and Granger causality tests. This talk is based on joint research with Ines Wilms (Cornell), Luca Barbaglia (KU Leuven) and Sarah Gelper (TU Eindhoven).