The interaction of x-rays with the electrons in atoms is dominated by Thomson scattering. The resonant contributions in the scattering amplitude play the role of perturbations, which may be important in special applications. On the contrary, the interaction of x-rays and atomic nuclei is a case of pure resonance scattering. A Mossbauer nucleus presents a simple resonating two level system. Scattering of x-rays by a nuclear ensemble is characterized by the formation of collective coherent nuclear excitations - nuclear excitons. The sharpness of the nuclear resonance correlates to a long lifetime of the nuclear excited state, which Lies in the range 10(-5) - 10(-9)s. Pulsed synchrotron radiation (SR) sources provide the best possibility to observe the time evolution of x-ray nuclear scattering. Since excitation by a SR pulse is almost instantaneous compared to the characteristic nuclear lifetimes, the two stages of the scattering process, excitation and decay are well separated in time: the nuclear excitations exhibit a free, delayed decay. Both the time differential and time integrated intensities of the delayed radiation deliver rich information about the states of nuclear ensembles. Owing to specific properties of nuclear transitions unique information concerning crystalline magnetic and electric fields, magnetic and electric phase transitions, internal dynamics, such as thermal vibrations, diffusion, fluctuations, relaxation, etc., can be obtained by studying synchrotron resonant nuclear scattering. The physical principles of the new experimental technique are described and applications are illustrated by recent experiments.