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We present an overview of both experimental and theoretical results in the eld of resonant scattering of tunable soft and hard X-ray radiation, with a main focus on the closely related processes of resonant inelastic X-ray scattering (RIXS) and resonant Auger scattering (RAS). The review starts with an overview of fundamental dynamical aspects of RIXS illustrated for dierent systems. We give a detailed analysis of case studies with increasing complexity, considering both gas phase and condensed matter (liquids and solids) applications. In the review, we outline the most important achievements in investigations of coupled electron-nuclear dynamics and structural aspects in studies of liquids and solids over the last two decades. To give a perspective on the insights from RIXS and RAS, we briey discuss the X-ray results against the background of complementary experimental techniques like vibrational infrared absorption and Raman spectroscopy, as well as small-angle X-ray and neutron scattering. Finally, recent achievements in time-resolved studies based on X-ray free-electron lasers (XFEL) are described briey. X. Recoil eect: translational and rotational motion 22 A. Preparation of initial state for Auger decay 22 B. Experimental observation of recoil induced non equilibrium distribution over velocities 22 C. Dynamical rotational Doppler eect 22 XI. RIXS of liquids 23 A. RIXS of liquid acetone: Mechanisms of line broadening 24 B. Nuclear dynamics in RIXS of free water molecules 24 1. Quasi-elastic RIXS of free water molecules 26 2. Dynamical origin of the splitting lone pair RIXS resonance in gas phase water and methanol 26 C. RIXS of liquid water and methanol 27 1. RIXS vs X-ray and neutron scattering, IR, Rayleigh-Brillouin scattering and XAS 28 2. Dynamical origin of the lone-pair peak splitting in RIXS of liquid water and methanol 28 3. Role of hydrogen bond on vibrations and uctuations of OH potential energy curves. RIXS vs IR spectroscopy 29 D. Anomalous role of hydrogen bond on RIXS of liquid acetic acid 30 XII. RIXS in studies of correlated materials 31 A. Charge transfer 32 XIII. Resonant elastic X-ray scattering in solids. Orbital and charge ordering 33 A. Hard X-ray region. Orbital ordering vs Jahn-Teller distortion 34 B. Charge density waves in the cuprates 35 C. RIXS from low dimensional systems 35 D. Dynamics of multi-spinon excitation in RIXS 37 XIV. Nonlinear phenomena in strong eld of XFEL pulses 37 A. Stimulated RIXS, four-wave mixing, pulse compression, superuorescence, suppression of the Auger decay channel 37 B. Second Harmonic generation 38 C. Superuorescence and superradiance 39 D. Self-induced X-Ray transparency 39 E. Time-resolved RIXS studies of magnetic excitations 40 F. Dynamics of liquid-liquid phase transitions revealed by ultrashort optical pump and XFEL probe pulses 40 G. Time-resolved UV pump RIXS probe spectroscopy to monitor reaction paths in chemical processes in solution 40 XV. Summary 42 List of Symbols and abbreviations 43 ACKNOWLEDGMENTS 44 References 44I. INTRODUCTION Scatte...