High wind speeds pose a threat to the integrity of structures, particularly those at exposed sites such as bridges, wind turbines and radio masts. In any design project for large structures, safety considerations must be balanced against the additional cost of 'over-design'. Accurate estimation of the occurrence of extreme wind speeds is an important factor in achieving the correct balance. Such estimates are commonly expressed in terms of the quantile value X T , i.e., the maximum wind speed which is exceeded, on average, once every T years, the return period. Typically, for most users of wind data, estimates of the 50-year return period gust or wind speed are required, based on 10-20 (and often fewer) available years of observations. For this situation, the data are generally fitted to a theoretical distribution in order to calculate the quantiles. Fisher & Tippett (1928) showed that if a sample of n cases is chosen from a parent distribution, and the maximum (or minimum) of each sample is selected, then the distribution of the maxima (or minima) approaches one of three limiting forms as the size of the samples increases. Gumbel (1958) argued that, in the case of floods, each year of record constitutes a sample with 365 cases and that the annual extreme flood is the maximum value of the sample. Thus, the Fisher-Tippett distributions could be fitted to the set of annual maxima. This is the basis of all classical extreme value theory. The aim is to define the form of the limiting distribution and estimate the parameters, so that values of X T can be calculated.Here, we review and summarize the portion of the extensive literature on extreme value theory relevant to the analysis of wind and gust speed data. The review is carried out with reference to the requirements of a user seeking to select and apply a method appropriate to a particular real data set. We discuss first the available techniques and then the choices required for successful selection and implementation. The methods are organized broadly according to the length of the time series of observations available for analysis, beginning with those which require longer data sets, and moving towards those developed for use with short-duration series. The length of the observational data set is often a problem for those wishing to calculate extreme wind speed quantiles but is a common concern for users of geophysical data, and a substantial literature exists on estimation of extremes from short time series.Note that we do not consider here the matter of anemometer exposure. As with all analyses of wind data, the results of an extreme value analysis will be flawed if the data on which they are based are taken from an anemometer with a non-standard exposure (e.g., sheltered in one or more directions, or at a height above the ground different from the 10 m standard).Meteorol. Appl. 6, 119-132 (1999) A review of methods to calculate extreme wind speeds