Some of the many statistical aspects of floods are discussed and some new results are given on a number of features. The probability theory of extreme values is briefly reviewed and its potential for applications outlined. The peaks–over–threshold method of estimation is compared with the direct use of annual maxima and some theoretical comparisons of efficiency are given. The effect of trend on the distribution of maxima is analysed in terms of a simple theoretical model distinguishing the effects of trend in mean level and of trend in dispersion. An empirical Bayes method for pooling information from a number of sources is described and illustrated, and related to the procedures recommended in the Flood estimation handbook. In the final section, a range of further issues is outlined.