An expanding literature articulates the view that Taylor rules are helpful in predicting exchange rates. In a changing world, however, Taylor rule parameters may be subject to structural instabilities, for example in the aftermath of the Global Financial Crisis. This paper forecasts exchange rates using Taylor rules with Time-Varying Parameters (TVP) estimated by Bayesian methods. Focusing on the data from the crisis, we improve upon the random walk for at least half, and for as many as seven out of 10, of the currencies considered. Results are stronger when we allow the TVP of the Taylor rules to differ between countries.