Due to the ever-increasing interest in cryocrystals in scientific and applied problems, a thorough study of their various properties and characteristics is necessary. The analysis of experimental anomalies in a number of physical properties of quantum cryocrystals (helium, hydrogen and methane) is presented in the low-temperature region. In this temperature region thermal fluctuations decrease sharply, whereas the role of quantum fluctuations stays dominant. This is manifested not only in the translational motion of atoms or defects in such crystals (as helium, neon), but also in the rotational degrees of freedom, for example, in the properties of solid methane and hydrogen.