In the academic literature, a broad consensus appears to be emerging in favour of so-called "flexible inflation targeting" stragegies for monetary policy. The late 1980s and 1990s saw several central banks adopt some version of inflation targeting. However, the adoption of inflation targeting has not been universal. In particular, neither the U.S. Federal Reserve nor the European Central Bank have adopted such an approach. This paper offers a critical survey of the academic literature on inflation targeting (and the (related) Taylor rules for monetary policy), organised around a typology of inflation targeting frameworks developed in section 2.