This paper reviews recent advances in the specification and estimation of Bayesian Vector Autoregressive models (BVARs). After describing the Bayesian principle of estimation, we first present the methodology originally developed by Litterman (1986) and Doan et al. (1984) and review alternative priors. We then discuss extensions of the basic model and address issues in forecasting and structural analysis. An application to the estimation of a system of time-varying reaction functions for four European central banks under the European Monetary System (EMS) illustrates how some of the results previously presented may be applied in practice.