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Since their discovery more than 100 years ago, X-rays have transformed our understanding of the fundamental structure of matter. They have become an indispensable tool for materials science, biology, chemistry, physics, and many related fields. The recent emergence of X-ray free-electron lasers (XFELs) represents a revolution in X-ray science that promises to transform the field for the 21st century. XFELs can generate coherent X-ray beams with both peak brightness and average brightness that are many orders of magnitude higher than those of any other X-ray source. Pulse durations can be as short as 0.2 femtoseconds (fs) to 200 fs, with a time-bandwidth product close to the Fourier transform limit, over a spectral range from 0.2 to >30 keV. New science frontiers enabled by XFELs include (i) sensitive probing of structural dynamics in matter on the fundamental timescales and length scales of atomic motion, (ii) element-specific probing of electronic structure and charge dynamics on fundamental timescales of electronic motion, and (iii) powerful new approaches for unravelling the coupling between electronic and atomic structural dynamics that underpin the properties and function of matter. This chapter outlines the distinguishing capabilities of XFELs and highlights their science impact across broad fields of science.

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