Although clonal species are dominant in many habitats, from unicellular organisms to plants and animals, ecological and particularly evolutionary studies on clonal species have been strongly limited by the difficulty in assessing the number, size and longevity of genetic individuals within a population. The development of molecular markers has allowed progress in this area, and although allozymes remain of limited use due to their typically low level of polymorphism, more polymorphic markers have been discovered during the last decades, supplying powerful tools to overcome the problem of clonality assessment. However, population genetics studies on clonal organisms lack a standardized framework to assess clonality, and to adapt conventional data analyses to account for the potential bias due to the possible replication of the same individuals in the sampling. Moreover, existing studies used a variety of indices to describe clonal diversity and structure such that comparison among studies is difficult at best. We emphasize the need for standardizing studies on clonal organisms, and particularly on clonal plants, in order to clarify the way clonality is taken into account in sampling designs and data analysis, and to allow further comparison of results reported in distinct studies. In order to provide a first step towards a standardized framework to address clonality in population studies, we review, on the basis of a thorough revision of the literature on population structure of clonal plants and of a complementary revision on other clonal organisms, the indices and statistics used so far to estimate genotypic or clonal diversity and to describe clonal structure in plants. We examine their advantages and weaknesses as well as various conceptual issues associated with statistical analyses of population genetics data on clonal organisms. We do so by testing them on results from simulations, as well as on two empirical data sets of microsatellites of the seagrasses Posidonia oceanica and Cymodocea nodosa. Finally, we also propose a selection of new indices and methods to estimate clonal diversity and describe clonal structure in a way that should facilitate comparison between future studies on clonal plants, most of which may be of interest for clonal organisms in general.