It comprises multiple contributions to solid state physics starting early on in the field of structural phase transitions in perovskite oxides with emphasis on their investigation using electron paramagnetic resonance (EPR). As a result, essential knowledge was gained on the order parameter of phase transition and the driving mechanism. He coined the term quantum paraelectricity to refer to the suppression of the expected transition to a polar state in SrTiO 3 , which has raised enormous interest in the research community. Further EPR studies by M¨uller are related to the resonance of ions corresponding to impurities in diverse perovskites and related crystals and, thereby, the discovery of experimentally negative U-centers that were later on established theoretically.The Jahn-Teller effect attracted his attention early on and played a key role in the discovery of high-temperature superconductivity in cuprates, where the Jahn-Teller polaron is especially at the heart of this phenomenon. The polaron has also been shown to be vital in Fermi glasses, LaBaNiO 4 , and doped polythiophene. The concept of the Jahn-Teller polaron in connection with perovskite oxides inspired M¨uller to search for superconductivity in these compounds which-as everybody knows-was successful. In 1986, together with Georg Bednorz, he discovered high-temperature superconductivity in LaBaCuO, with the highest ever observed transition temperatures at ambient pressure-a discovery which was awarded with the Nobel prize only one year later. This discovery caused an enormous worldwide breakthrough in basic research as well as in possible applications. In order to explain these findings, M¨uller suggested the polaron concept and bipolaron condensation.In order to verify this concept, he proposed searching for unconventional isotope effects which have indeed been observed in cuprates.