This paper presents several indices to describe multivariate diversity and evenness. Multivariate generalizations of the Gini-Simpson index and the Rosenbluth index are proposed tomeasure diversity. A multivariate Gini ratio is also presented to measure evenness. These indices extend the usual univariate measures; they reflect not only the diversity of marginal distributions but also the dependence structure of abundance. The indices fulfill desirable measurement properties and are consistent with certain orderings of multivariate distributions. An order of concentration surfaces and a majorization order are also surveyed shortly.