Extreme conditions involving the simultaneous application of high pressures and high temperatures can induce unexpected chemical compositions, atom arrangements and electronic structures leading to new classes of materials with unique properties. We are specialized in utilizing large-volume press methodology for the synthesis of new materials at pressures up to about 25 GPa. For this p,T formation conditions and the phase stabilities of products are mapped from in situ synchrotron diffraction studies. Current efforts center round hydrogen rich (higher hydride) and oxygen rich (higher oxide) materials. Higher hydrides are predicted to possess interesting properties relating to superconductivity, ion conductivity and hydrogen storage. The expectations for higher oxides are new magnetic behaviors and magneto-electronic properties based on the unusual dn and fn electron configuration of involved transition metals and lanthanides. We regularly apply computational methods in tandem to our experimental efforts. In particular, crystal structure prediction (CSP) methodology is invaluable for the identification of compounds and structures in in situ diffraction patterns. Also, predicted compositions and structures will then serve as valuable input for evaluating and guiding the experiments. CSP calculations are typically performed for the pressure range 0-30 GPa. The stability of the obtained compounds are then checked using hull line and phonon calculations. For predicted stable phases (p,T)-dependent electronic structure and phonon calculations are performed. In addition, magnetic structures and their p,T dependence may be characterized by computation. For the allocation here applied for we will perform CSP for the Sr-Au-H system and phase stability calculations for the recently established series of hydrogen-rich complex transition metal hydrides Na3THn (T = Cr – Cu, n = 9 – 4). Further we will continue with challenging CSP for the binary systems Ni-O, Cu-O and Cu-F for which standard procedures are not applicable because of strong correlation effects.