Interactions between B‐cell antigen receptors (BCRs) and their ligands have a complexity and variability that is unparalleled within known biology. Each developing B cell undergoes gene rearrangements to generate a BCR encoded by a unique pair of immunoglobulin (Ig) variable region genes, which serves to make the antigen‐binding capabilities of primary BCRs incredibly diverse. Further diversification of the BCR repertoire takes place when antigen‐activated B cells enter the germinal center (GC) response and undergo somatic hypermutation (SHM) of their Ig variable region genes. To develop optimal antibody responses against foreign antigens, the key B‐cell survival and differentiation decisions made in the GC are based primarily on the affinity of the BCR (and therefore subsequent antibodies) for foreign antigen. However, the secondary diversification of BCRs by SHM also carries the risk of generating new self‐reactive specificities and thus autoantibody production. Herein, we review the role of antigen affinity/avidity in controlling pivotal events both leading up to and during the GC response. The emergence of self‐reactivity during the GC response is also examined, with particular focus on the threat posed by cross‐reactive GC B cells that bind both self and foreign antigen.