This article introduces the eigensystem autoregression (EAR) framework, which allows an AR model to be specified, estimated, and applied directly in terms of its eigenvalues and eigenvectors. An EAR estimation can therefore impose various constraints on AR dynamics that would not be possible within standard linear estimation. Examples are restricting eigenvalue magnitudes to control the rate of mean reversion, additionally imposing that eigenvalues be real and positive to avoid pronounced oscillatory behavior, and eliminating the possibility of explosive episodes in a time-varying AR. The EAR framework also produces closed-form AR forecasts and associated variances, and forecasts and data may be decomposed into components associated with the AR eigenvalues to provide additional diagnostics for assessing the model.