Recent advances in laser technology, with the development of extremely short-pulse, high-intensity lasers, have opened doors to new areas in atomic physics. By focusing light from an intense, short-pulse laser into a gas jet, the emission of high-order harmonics of the laser frequency has been studied. The aim of this work has been two-fold: to better understand the underlying physics of the harmonic generation process and to demonstrate the use of the generated radiation in novel applications. Experiments have been performed using both femtosecond and picosecond laser systems. The temporal coherence of harmonic radiation has been measured and characterised. We have shown that the far-field pattern of high-order harmonics separates into two spatial regions with different coherence properties. These features have been related mainly to the single-atom response, but also influenced by different phase-matching conditions. For the central region we find long coherence times, close to the expected duration of the harmonic pulse. The harmonic spectra from molecular gases have been investigated. They were found to be very similar to those obtained in rare gases, with a plateau and a cutoff whose location is strongly correlated to the ionisation potential. The conversion efficiency in the investigated molecules was not higher than that in one of the rare gases suitable for the specific wavelength region. Applications using harmonic radiation as a narrowband, coherent XUV source have been performed. Spectroscopic measurements have been made using harmonic radiation produced from a tunable laser source. Lifetimes of highly excited states in CO have been determined and the energy dependence of the photo-ionisation cross-sections of highly excited states in He has been measured. XUV interferometry using harmonic radiation has been demonstrated with femtosecond resolution, using the 11th harmonic of a femtosecond laser, to probe the spatial variation of the electron density in a plasma.