The narrow nuclear resonances of Mössbauer isotopes constitute almost ideal two-level systems to study cooperative effects in the interaction of x-rays with matter. Embedding an ensemble of resonant Mössbauer nuclei into a planar cavity facilitates the excitation of superradiant oscillatory eigenmodes via pulses of synchrotron radiation. These modes exhibit a large collective Lamb shift that can be controlled via the excitation conditions and the cavity geometry. Cooperative emission in connection with the radiative coupling of two resonant ensembles in a cavity leads to electromagnetically induced transparency (EIT). This contribution gives a review on cooperative effects in nuclear resonant scattering of synchrotron radiation. Special emphasis is given to the basic principles of recent experiments that led to the observation of the collective Lamb shift and EIT with nuclear resonances in the regime of hard x-rays.