In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude mmax from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of mmax. In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about mmax unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to mmax, are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of mmax, and this results in unacceptably high uncertainties. As a consequence, estimators of mmax in a fault zone, which are based solely on earthquake‐related information from this region, have to be dismissed.