A rough surface may be described by its statistical moments. The second order one, which is called the autocovariance function, is significant in that it makes it possible to describe a rough surface by means of two parameters, namely the root-mean-square surface roughness height and the autocovariance length. It is shown that some complications arise when the definition of the autocovariance length for not perfectly randon surfaces is considered. Solutions are proposed to overcome them. At the present time the knowledge of higher moments is needed in the framework of theories about surface plasmons and polaritons. The problem of the determination of third and fourth order moments is considered for rough surfaces. Results are compared to what has to be expected for a gaussian process (in this case the third order moment is zero and the fourth order moment satisfies the standard relation involving the sum of products of second order moment taken two-by-two different in all possible ways. At last it is shown that other approaches exist that enable us to characterize random rough surfaces. In particular the minimal spanning tree, which is a graph constructed on the set of points representing the position of features on a surface, turns out to be a powerful tool to statistically study order and disorder in the distribution of these features.