As reputation and credibility are important elements for monetary policy effectiveness, the paper aims at exploring the concepts of both and its importance in a context where central banks policies are not neutral, that is, monetary policy affects real and nominal variables. The paper seeks to contribute with a new analysis of how the sort of reputation developed by the monetary authority affects the state of expectations, and then the economic performance, enabling a particular situation that we call "credibility trap" - which makes monetary policy ineffective to affect real activity when necessary. Although the paper presents some similarities to the orthodox approach regarding both reputation and credibility's importance for central banks and its policies, it is different from the orthodox approach speaking of distinct forms of monetary policy recommendations and the sort of reputation that it recommends to be developed.