Although there are rules and regulations for “regulatory” asbestos group minerals including amphibole group minerals of actinolite, amosite, anthophyllite, crocidolite, tremolite; and serpentine group mineral of chrysotile, there is no rule and regulation for naturally occurring “non-regulatory” asbestos group minerals, which include richterite, winchite, fluoro-edenite, balangeroite, carlosturanite, gageite, arfvedsonite, and magnesio-arfvedsonite. Very strong evidences for carcinogenicity of these minerals exist and cohorts of cancer patients have demonstrated risks associated with these minerals. However, some controversies still exist for the chrysotile asbestos regulated by some organizations such as WHO, World Trade Organization, United Nations, US EPA, International Labor Organization, and EU Countries. Therefore, we propose that all “non-regulated” asbestos group minerals and the chrysotile should be re-evaluated. Accurate characterizations of chemical composition, morphology, structure, and defects are necessary in order to find out mechanism(s) of carcinogenicity of all asbestos group minerals. Detail morphological and chemical characterization of individual asbestos group minerals in micro- and nano-scale may help to evaluate its true carcinogenetic mechanism(s), and consequently prevention and possibly treatment of related diseases. The amount of fibers inhaled, in terms of weight percents and numbers, need also be re-evaluated by mineralogists. Eventually, International Regulatory Agencies should oversea “positive” identification guidelines followed closely for non-regulatory asbestos group minerals.