AbstractThe h‐index is a popular bibliometric indicator for assessing individual scientists. We criticize the h‐index from a theoretical point of view. We argue that for the purpose of measuring the overall scientific impact of a scientist (or some other unit of analysis), the h‐index behaves in a counterintuitive way. In certain cases, the mechanism used by the h‐index to aggregate publication and citation statistics into a single number leads to inconsistencies in the way in which scientists are ranked. Our conclusion is that the h‐index cannot be considered an appropriate indicator of a scientist's overall scientific impact. Based on recent theoretical insights, we discuss what kind of indicators can be used as an alternative to the h‐index. We pay special attention to the highly cited publications indicator. This indicator has a lot in common with the h‐index, but unlike the h‐index it does not produce inconsistent rankings.