An introduction to high-power lasers and strong-field laser-atom inter
actions is given, and the main experimental and theoretical results co
ncerning high-order harmonic generation are reviewed. The single atom
response as well as the macroscopic phase-matching effect is discussed
. The formation and extent of the characteristic plateau in the harmon
ic spectra are discussed in terms of a physical picture valid in the t
unnel-ionisation regime. Very high-order harmonics have been reported,
opening the way to construct bright sources of coherent radiation in
the XUV and soft X-ray ranges. Some examples of possible applications
of such a source are presented.