In vertebrates, the world of antigenic motifs is matched to large populations of lymphocytes through specific recognition of an epitope by a given receptor unique to a lymphocyte clone. The concept of immune repertoire was proposed to describe this diversity of lymphocyte receptors - Ig and TCR - required by the network of interactions. The immune repertoires became useful tools to describe lymphocyte and receptor populations through the development of the immune system and in pathological situations. Recently, the development of mass technologies made possible a comprehensive survey of immune repertoires at the genome, transcript and protein levels, and some of these techniques have been already adapted to TCR and Ig repertoire analyses. Such approaches generate very big datasets, which necessitates complex and multi-parametric annotations in dedicated databases. They also require new analysis methods, leading to the integration of structure and dynamics of the immune repertoires, at different time scales (immune response, development of the individual, evolution of the species). Such methods may be extended to the analysis of new classes of adaptive-like receptors, which were recently discovered in different invertebrates and in agnathans. Ultimately, they may allow a parallel monitoring of pathogen and immune repertoires addressing the reciprocal influences that decide for the host survival or death. In this review, we first study the characteristics of Ig and TCR repertoires, and we examine several systematic approaches developed for the analysis of these "classical" immune repertoires at different levels. We then consider examples of the recent developments of modeling and statistical analysis, and we discuss their relevance and their importance for the study of the immune diversity. An extended view of immune repertoires is proposed, integrating the diversity of other receptors involved in immune recognition. Also, we discuss how repertoire studies could link pathogen variation and immune diversity to reveal regulatory patterns and rules driving their co-diversification race.