Reports published in the last 25 years on the synthesis of carbon-based materials significantly superior to diamond in hardness and elastic properties have been critically examined, and three groups of recently appearing myths have been analyzed. The first group concerns the possibility of producing materials with bulk moduli much higher than that of diamond. The second group regards to «experimentally measured» hardness significantly higher than that of diamond. Myths of the third group state that quantum confinement effects supposedly provide «theoretical» foundations for a several-fold increase in the hardness of covalent materials. The fundamental impossibility of synthesizing materials with elastic moduli noticeably exceeding those of diamond under normal conditions has been demonstrated. The problems of hardness measuring have been discussed; it was shown that the formation of obstacles for motion of dislocations can allow increasing the measured hardness of superhard materials by 20-40%. It was demonstrated that other hypothetical ways for hardness increase, e.g. owing to quantum confinement have no any real physical grounds. The superior mechanical properties of diamond are due to reliably established physical laws. Accordingly, any statements on the possibility of obtaining materials with elastic characteristics and/or hardness several times higher than the corresponding values for diamond cannot be considered as scientifically reliable.