Our activities are focused on microscopic theories describing physical phenomena in selected families of transition metal oxides. We are interested mainly in phenomena related to the strongly correlated nature of valence electrons in these compounds that manifests itself e.g. in peculiar magnetic properties or unconventional superconductivity. These phenomena can be captured at the level of effective models such as the Hubbard model, t-J model or spin models that we deal with using a number of methods ranging from analytical diagrammatic approaches up to extensive numerical simulations performed on supercomputers.