Seismic design of structures is currently based on the amplitude of ground motions caused by earthquakes expressed in terms of the acceleration or displacement response of SDOF oscillators. The duration of ground shaking is generally not considered. A review of the technical literature shows that some studies find a link between duration and structural demand, whilst others do not. Part of the reason for this disagreement is that there are different definitions of ground-motion duration and number of cycles; most of which are poorly correlated. The seismological characteristics that influence duration and number of cycles are reviewed and a new predictive equation is derived for bracketed duration. This shows that earthquake magnitude has the primary influence on ground-motion duration and number of cycles. Analysis of an 8-storey reinforced concrete wall frame building shows that accelerograms can be linearly scaled by factors of 10 without causing a bias (over- or under-estimation) of the response, provided they are initially selected to match the earthquake magnitude and spectral shape. A new method of adjusting accelerograms using wavelets to match smooth elastic response spectra at multiple damping levels is developed. This enables structural response to be predicted with greater confidence and with fewer analyses than possible using accelerograms selected by seismological criteria and linearly scaled to match the response spectrum. An extensive study of strength and stiffness degrading masonry structures is conducted. This shows that ground-motions with longer duration, for a given level of spectral acceleration, cause greater damage. Analysis of a reinforced concrete wall frame building with spectrally matched accelerograms demonstrates that the influence of the ground-motion duration principally depends on the damage metric used; peak response measures (such as inter-storey drift) are not influenced by duration, whilst hysteretic energy and fatigue damage measures are generally positively correlated with ground-motion duration.