Structural vector-autoregressive models are potentially very useful tools for guiding economic policy. I present a recently developed method to estimate and identify the causal structure underlying the data generating process. The method, which is based on graphical models, exploits conditional independence tests among estimated VAR residuals to infer the causal relationships among contemporaneous variables. I first show how this method works in the Gaussian linear setting. Then I present some developments for both the linear non-Gaussian and nonlinear settings.