The response of deep foundations to repeated dynamic loading has been a subject of considerable interest in recent years in relation to the seismic design of important structures such as nucIear power plants, offshore structures and vibrating machines, etc, In spite of significant efforts on the part of theoretical and experimental researchers and the avai!ability of powerful computers, because ofthe complex interaction effects in the superstructure-foundation-soi! system, and - more importantly - the inelastic nature of the soil behaviour, exact solutions to the problem are stilI not available. In current practice the engineer is necessarily faced with simplified, uncoupled, iterative procedures valid for specific cases; the choice of a methodology associated with the definition of relevant soil properties is stilI fundamentaly empirica!. The review ancl discussion of possible theoretical approaches are here mainly oriented toward their applicability and shortcomings in light of the more recent experimental and theoretical developments. Basic aspects related to geotechnical investigations and the cletennination of soil properties are pointecl out, as well as the mai n factors that govern important phenomena such as clegraclation of soi! characteristics due to cycIic loacling ancl clepenclence of stiffness ancl strength on rate of loading. Advantages associated with the use centrifuge ancl full scale moclels both for research ancl for practical applications are inclicatecl, especially in presence ofvery complex nonlinear boundary problems such as those representecl by large pile group foundations.