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The strontium ruthenates of the RuddlesdenPopper series have attracted much interest in the last two decades due to the variety of their different ground states. These states, ranging from unconventional superconductivity over metamagnetic behavior with a new lowtemperature phase to itinerant ferromagnetism, are often in close competition and thus crucially depend on system parameters and crystal purity. The discussion in this work concentrates on selected exotic phenomena in the ruthenates which are explored within different theoretical frameworks. In a first part, it is shown how the caxis transport in the singlelayer compound can be understood in terms of a two to onedimensional crossover within the basal plane and the associated loss of spectral weight. The second part deals with the bilayer ruthenate. In particular, the directional anisotropy of the phase diagram to magnetic fields is explained with a staggered spinorbit coupling stemming from the rotation of the oxygen octahedra. The last part investigates the effect of staggered noncentrosymmetricity within a regular sublattice structure on superconductivity in some analogy to the case of antiferromagnetic crystals.
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