The recent discoveries of the long-lived high spin super- and hyperdeformed isomeric states and their unusual radioactive decay properties are described. Based on their existence a consistent interpretation is given to the production of the long-lived superheavy element with Z = 112, via secondary reactions in CERN W targets, and to the low energy and very enhanced alpha-particle groups seen in various actinide fractions separated from the same W target. In addition, consistent interpretations are suggested for previously unexplained phenomena seen in nature. These are the Po halos, the low-energy enhanced 4.5 MeV alpha-particle group proposed to be due to an isotope of a superheavy element with Z = 108, and the giant halos.