  The adaptive immune system recognizes antigens via an immense array of
antigen-binding antibodies and T-cell receptors, the immune repertoire. The
interrogation of immune repertoires is of high relevance for understanding the
adaptive immune response in disease and infection (e.g., autoimmunity, cancer,
HIV). Adaptive immune receptor repertoire sequencing (AIRR-seq) has driven the
quantitative and molecular-level profiling of immune repertoires thereby
revealing the high-dimensional complexity of the immune receptor sequence
landscape. Several methods for the computational and statistical analysis of
large-scale AIRR-seq data have been developed to resolve immune repertoire
complexity in order to understand the dynamics of adaptive immunity. Here, we
review the current research on (i) diversity, (ii) clustering and network,
(iii) phylogenetic and (iv) machine learning methods applied to dissect,
quantify and compare the architecture, evolution, and specificity of immune
repertoires. We summarize outstanding questions in computational immunology and
propose future directions for systems immunology towards coupling AIRR-seq with
the computational discovery of immunotherapeutics, vaccines, and
immunodiagnostics.
