This paper is part of the special publication No. 155, Fractures, fluid flow and mineralization. (eds K.J.W. McCaffrey, L. Lonergan and J.J. Wilkinson). The thickness and spacing systematics of 30 line samples of vein arrays at ten localities have been analysed. The analytical methods were tested on four synthetic data sets. The synthetic and natural data sets were each analysed with respect to: cumulative thickness v. distance; thickness population; spacing population; the coefficient of variation of spacing, which measures clustering; the mass function, which measures the scaling of strain heterogeneity. A fundamental distinction is apparent between stratabound arrays, vein arrays in layered rocks where the veins are confined to individual mechanical units, and non-stratabound arrays which occur in rock volumes lacking persistent crack-stopping discontinuities. The stratabound arrays show regular spacing controlled by layer thickness and non-power-law thickness distributions. The non-stratabound arrays are clustered and have power-law thickness distributions resulting from the lack of a controlling length scale. Exponents of the thickness distributions have a modal value of 0.8 and do not vary significantly with lithology. Ore mineralization is favoured in non-stratabound arrays as they are more likely than stratabound arrays to form large clusters connected to a remote fluid source.