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Besides the popularity of the h‐index, some criticism has been drawn and an enormous number of modifications and extensions of the h‐index have since appeared (Costas and Franssen 2018; Meho 2007; Schreiber 2007; Vinkler 2007; Adler et al. 2008; Schreiber et al. 2012; Waltman and van Eck 2012). The h‐index is not as objective as the research community would like it to be. By definition, it is biased in favor of mature researchers over younger researchers. A mature researcher with moderate research impact is expected to have a higher h‐index than a young researcher at the beginning of his or her career, even if the latter eventually develops into a researcher with a higher impact factor.

There are a number of other situations mentioned in the literature where the h‐index may provide misleading information about a researcher's impact and productivity. For example, the lack of sensitivity of the h‐index to the excess citations of the h‐core papers (the set of papers whose citations contribute toward h‐index) is a frequently noted disadvantage (Egghe 2006a,b,c; Kosmulski 2007). The h‐index does not take into account important factors that differentiate the ways research activity develops and is transferred, such as the distinction between research fields and specialties (van Leeuwen 2008). For example, an h‐index of 20 for an applied physicist would be a fair score, whereas the same figure would be wishful thinking for a theoretical mathematician.

Abramo et al. (2013) reveal yet another example of the problematic use of the h‐index for measuring research performance of institutions. The most profound argument against using the h‐index for ranking larger bodies (such as institutions, departments, etc.) is the influence of faculty size in calculating the h‐index value. Because the organizations are comprised of greatly varying numbers of faculty and research staff, the h‐index value is significantly affected. Thus, various modifications and extensions of the h‐index have appeared in literature starting almost immediately after its introduction.