I introduce the essential aspects of the eigensystem vector autoregression (EVAR), which allows VARs to be specified and estimated directly in terms of their eigensystem, using univariate examples for clarity. The EVAR guarantees non-explosive dynamics and, if included, non-redundant moving-average components. In the empirical application, constraining the EVAR eigenvalues to be real and positive leads to “desirable” impulse response functions and improved out-of-sample forecasts.