When a very intense Laser pulse, usually generated with a mode-locked laser and a regenerative amplifier (typically with chirped-pulse amplification), is focused into a gas (usually at reduced pressure), strong nonlinear interactions can lead to the generation of very high odd harmonics of the optical Frequency of the pulse, i.e., to an extreme form of nonlinear frequency conversion. This typically occurs at intensities of the order of 1014 W/cm2 or higher. Although only a tiny fraction of the laser power can be converted into higher harmonics, this output can still be useful for measurements down to wavelengths in the hard Ultraviolet or even the X-ray spectral region. Such high harmonics may thus be used instead of synchrotron radiation. They are also used to generate Pulses with attosecond durations in the extreme ultraviolet spectral region.