Rational expectations assume perfect, model consistency between beliefs and market realizations. Here we discuss behaviorally rational expectations, characterized by an observable, parsimonious, and intuitive form of consistency between beliefs and realizations. We discuss three case-studies. Firstly, a New Keynesian macro model with a representative agent learning an optimal, but misspecified, AR(1) rule to forecast inflation consistent with observed sample mean and first-order autocorrelations. Secondly, an asset pricing model with heterogeneous expectations and agents switching between a mean-reverting fundamental rule and a trend-following rule, based upon their past performance. The third example concerns learning-to-forecast laboratory experiments, where under positive feedback individuals coordinate expectations on non-rational, almost self-fulfilling equilibria with persistent price fluctuations very different from rational equilibria.