The review reports recent progress in experimental and theoretical studies of structure and properties of the C6H12N2 molecule (DABCO) in metal-organic frameworks M2(C8H4O4)2 C6H12N2, where M = Co, Ni, Cu, Zn (M-DMOFs), as well as in the gas and crystalline phases. M-DMOFs belong to a new class of compounds which are considered promising materials for sorption, catalysis, selective separation, and demonstrate other remarkable properties. We review recent research on phase transitions and effect of guest molecules on properties of M-DMOFs. Thermodynamic and nuclear magnetic resonance studies of M-DMOFs indicate quantum tunneling between twisted forms (chiral isomers) of the DABCO molecule with D3 symmetry, which stops at certain low temperature. This opens an opportunity for study and control of balance between chiral isomers.