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What are the implications of simple deviations from rational expectations for macroeconomic dynamics, monetary policy, consumption decisions and labor markets? Which biases underly even sophisticated survey expectations? I aim to answer these questions by building upon simple mathematical models of expectations that are boundedly rational and generate some disagreement across expectations. While monetary policy should be extraordinarily hawkish if it wants to control inflation under such expectations, it also generates substantial dispersion in consumption and wealth. Further, the sluggishness of labor market variables may be explained by sluggish expectations that affect, for instance, wage bargaining. Finally, expectations of professional forecasters are intrinsically persistent, depend on the last observed consensus forecast and also extrapolate current news more than would be rational.