A brief introduction into computational methodology and preliminary results for spectroscopic (excitation energies, vibrational frequencies in ground and excited electronic states) and thermodynamic (stability constants, standard enthalpies and entropies of complexation reactions) properties of some 1:1, 1:2 and 1:3 uranyl sulphato- and selenato- complexes in aqueos solutions will be given. The relativistic effects are included via Effective Core Potential (ECP), electron correlation via (TD)DFT/B3LYP (dispersion interaction corrected) and solvation is described via explicit inclusion of one hydration sphere beyond the coordinated water molecules. We acknowledge limits of this approximate description – more accurate calculations (ranging from semi-phenomenological two-component spin-orbit coupling up to four-component Dirac-Coulomb-Breit hamiltonian) and Molecular Dynamics simulations are in preparation. The computational results are compared with the experimental results from Time-resolved Laser-induced Fluorescence Spectroscopy (TRLFS) and UV-VIS spectroscopic studies (including our original experimental research on this topic). In case of the TRLFS and UV-VIS speciation studies, the problem of complex solution spectra decomposition into individual components is ill-conditioned and hints from theoretical chemistry could be very important. Qualitative agreement between our quantum chemical calculations of the spectroscopic properties and experimental data was achieved. Possible applications for geochemical modelling (e.g. safety studies of nuclear waste repositories, modelling of a future mining site) and analytical chemical studies (including natural samples) are discussed.