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An overview is given of the different indices used, since their introduction in the 60's, for the determination of diversity in biological samples and communities. The most commonly used indices are based on the estimation of relative abundance of species in samples. Relative abundance can also be used for either a graphical or a mathematical representation of species-abundance relationships, from which diversity indices can be deduced as well. Most common in the literature are indices either describing the richness or species number and the evenness or partitioning of individuals over species or a combination of both. The most commonly used diversity indices can be grouped in a coherent system of diversity numbers developed by HILL (1973) that includes species richness. the Simpson index and a derivation of the Shannon-Wiener index as special cases. In this system species are different only when their abundance is different. Therefore, during the last decade a number of indices have been developed that take into account the taxonomic position, trophic status or body size of the species. There is as yet no consensus as to the use of evenness indices. We apply the condition that evenness should be independent of species richness (HEIP, 1974). The number of potential evenness indices is then strongly reduced. It is argued that the calculation of diversity or evenness indices should simply serve as description of community structure and be complemented with information on ecological functioning.