Central bank communication plays an important role in shaping market participants' expectations. This paper studies a simple nonlinear model of monetary policy in which agents have incomplete information about the economic environment. It shows that agents' learning and the dynamics of the economy are heavily affected by central bank transparency about its policy rule. A central bank that does not communicate its rule can induce 'learning equilibria' in which the economy alternates between periods of deflation coupled with low output and periods of high economic activity with excessive inflation. More generally, initial beliefs that are arbitrarily close to the inflation target equilibrium can result in complex economic dynamics, resulting in welfare-reducing fluctuations. On the contrary, central bank communication of policy rules helps stabilize expectations around the inflation target equilibrium.