Discovered during the last three decades after the Tolbachik eruption (1975-76, Kamchatka, Russia), new volcanic exhalative minerals exhibit a variety of crystal structures. Several of these minerals contain oxocentered tetrahedra (for example OCu₄) as the most rigid element of their crystal structure. These tetrahedra can be linked in a number of ways to build chains, layers or three dimensional frameworks. Many of these natural compounds (oxygen-containing compounds: oxides, selenates, arsenates, vanadates etc.) also contain transition metals in magnetically active oxidation states, and show interesting magnetic properties. The relations between crystal structures and magnetic properties can be investigated by combining experimental (x-ray diffraction analysis, measurement of magnetic susceptebility and specific heat at low temperatures) with theoretical methods (DFT calculations) and subsequent modeling (tight-binding models, Hubbard and Heisenberg models) of the relevant low energy states including strong electron-electron correlations.