X-Ray free-electron lasers (XFELs) generate nearly transversely coherent X-ray pulses over a wide wavelength range, from tens of nanometres to a fraction of one angstrom, with pulse durations from a few to hundreds of femtoseconds, and peak intensities from a few to 100 GW. Their unique and novel properties are opening a new area of scientific research in physics, chemistry, biology and materials sciences, at the length and time scale (angstrom–femtosecond) characteristics of atomic and molecular phenomena. In this paper, we review the physical principles, main characteristics and present status of XFELs. We also give a historical introduction on the subject and we briefly summarize novel developments in this exciting area of research.