The adaptive immune system is a natural defense mechanism that is able to detect and neutralize pathogens. The key molecules involved in this are the immune receptors expressed by B and T cells, collectively named immune repertoires. High-throughput sequencing has enabled unprecedented insight into the diversity of immune repertoires. However, there is a lack of clear guidelines for the quantitative characterization of the frequency distributions of immune repertoires. This thesis aims to provide such guidelines. Immune repertoires have been suggested to follow a power-law distribution. To investigate this claim, power-law distributions were fitted to experimental immune repertoire data. A generative model was implemented to further explore how immune repertoire frequency distributions may be distorted through subsampling and sequencing. Finally, this model was used to benchmark diversity and overlap measures that are often used to characterize immune repertoire data. Power-law distributions could not be fitted robustly to most of the experimental immune repertoire datasets. Through data simulation it was confirmed that heavy distortions of the clonal frequency distributions can be expected, particularly when the original repertoire contained many low-frequency clonotypes. These distortions also complicated the accurate estimation of diversity and overlap of immune repertoires based on subsampled sequence data. For most measures, the sequencing depth did not substantially impact the results. Furthermore, an increased sample size yielded more accurate results, but only if the underlying repertoire contained enough high-frequency clonotypes.