The ideas of directional distributions for random data are reviewed, in particular focussing on descriptive directional statistics to summarise these distributions. Consideration is then given to spatial variations in directional distributions; for example how does the directional distribution of wind direction vary across geographical space, and how may this be analysed? To investigate this issue, an approach to moving window-based smoothing of directional data is proposed, based on the application of a geographical kernel-based weighting scheme to find localised mean directions (and related statistics) to directions represented as complex numbers of magnitude one. Consideration is also given to the visualisation of the outputs of an analysis such as this. The paper concludes with two applications of the techniques proposed; an analysis of wind speeds across Europe drawn from NOAA observations, and an analysis of US inter-county net migration counts between 1985 and 1990. (c) 2005 Elsevier Ltd. All rights reserved.