We study the implications of the Fed's new policy framework of average inflation targeting (AIT) and its ambiguous communication. We show that AIT improves the trade-off between inflation and real activity by tilting the Phillips curve in a favorable way. To fully utilize this feature and maximize social welfare, the central bank has the incentive to deviate from AIT and implement inflation targeting ex post. Next, we rationalize the central bank's ambiguous communication about the horizon over which it averages inflation. Ambiguous communication, together with uncertainty about economic fundamentals, helps the central bank to gain credibility and improve welfare in the long run, in spite of the time-inconsistent nature of AIT.