This thesis studies the response of atoms and molecules to intense few-cycle laser pulses. It is the extremely high frequency dipole radiation generated from such a response that is of interest, both for its exploitation towards generating isolated attosecond pulses and because of the information such radiation contains concerning the laser pulse and electronic wavefunction responsible for its generation. Using a variety of models the process of high order harmonic generation in single atoms is studied in detail to reveal its underlying structure. The high harmonic spectrum is formed from bursts of radiation released every half-cycle of the laser field. The sensitivity of this half-cycle radiation to the precise waveform of the laser field is investigated. In particular the implications of these sensitivities to the stability of attosecond pulse production is studied. The work on single atom high harmonic generation is utilised towards investigations into the high harmonic generation from a volume of atoms. Propagation of the fields through such a volume greatly affects the final spectrum due to phase-matching. A new phenomenon is presented due to this phase-matching which leads tdthe manifestation of half-cycle cut-offs in the propagated spectra. A powerful new technique for measuring few-cycle pulse properties, utilising these half-cycle cut-offs, is developed and demonstrated. It is found capable of measuring the absolute carrier-envelope phase of the driving laser field to within 50 mrad, the highest accuracy of such a measurement achieved to date. The use of spatio-spectral filtering for isolating a half-cycle cut-off is proposed as a method for generating wavelength tunable attosecond pulses. Finally, work is carried out towards the development of a strong field approximation model capable of simulating high harmonic generation from molecules. Such a model is found to be suitable for such calculations and an interesting interference regime is commented on.