The human microbiota is a complex ecological community of commensal, symbiotic and pathogenic microorganisms harboured by the human body. Next-generation sequencing (NGS) technologies, in particular targeted amplicon sequencing of the 16S ribosomal RNA gene (16S-seq), are enabling the identification and quantification of human-resident microorganisms at unprecedented resolution, providing novel insights into the role of the microbiota in health and disease. Once microbial abundances are quantified through NGS data analysis, diversity indices provide valuable mathematical tools to describe the ecological complexity of a single sample or to detect species differences between samples. However, diversity is not a determined physical quantity for which a consensus definition and unit of measure have been established, and several diversity indices are currently available. Furthermore, they were originally developed for macroecology and their robustness to the possible bias introduced by sequencing has not been characterized so far. To assist the reader with the selection and interpretation of diversity measures, we review a panel of broadly used indices, describing their mathematical formulations, purposes and properties, and characterize their behaviour and criticalities in dependence of the data features using simulated data as ground truth. In addition, we make available an R package, DiversitySeq, which implements in a unified framework the full panel of diversity indices and a simulator of 16S-seq data, and thus represents a valuable resource for the analysis of diversity from NGS count data and for the benchmarking of computational methods for 16S-seq.