At any quantum critical point (QCP) with a critical magnetic field Hc, the magnetic Grüneisen parameter ΓH, which equals the adiabatic magnetocaloric effect, is predicted to show characteristic signatures such as a divergence, sign change and T /(H − Hc) scaling. We categorize thirteen materials, ranging from heavy fermion metals to frustrated magnets, where such experimental signatures have been found. Remarkably, seven stoichiometric materials at ambient pressure show Hc = 0. However, additional thermodynamic and magnetic experiments suggest that most of them do not show a zero-field QCP. While the existence of a pressure insensitive "strange metal" state is one possibility, for some of the materials ΓH seems influenced by impurities or a fraction of moments which are not participating in a frozen state. To unambiguously prove zero-field and pressure sensitive quantum criticality, a ΓH divergence is insufficient and also the Grüneisen ratio of thermal expansion to specific heat must diverge. arXiv:1609.02013v1 [cond-mat.str-el]