Antibody-mediated adaptive immunity must provide effective long-term protection with minimal adverse effects, against rapidly mutating pathogens, in a human population with diverse ages, genetics, and immune histories. In order to grasp and leverage the complexities of the antibody response, we advocate for a mechanistic understanding of the multiscale germinal center (GC) reaction - the process by which precursor B-cells evolve high-affinity antigen-specific antibodies, forming an effector repertoire of plasma and memory cells for decades-long protection. The regulatory dynamics of B-cells within the GC are complex, and unfold across multiple interacting spatial and temporal scales. At the organism scale, over weeks to years, the antibody sequence repertoire formed by various B-cell clonal lineages modulates antibody quantity and quality over time. At the tissue and cellular scale, over hours to weeks, B-cells undergo selection spatially distributed interactions with local stroma, antigen, and helper T-cells. At the molecular scale, over seconds to days, intracellular signaling, transcriptional, and epigenetic networks modulate B-cell fates and shape their clonal lineages. We summarize our current understanding within each of these scales, and identify missing links in connecting them. We suggest that quantitative multi-scale mathematical models of B-cell and GC reaction dynamics provide predictive frameworks that can apply basic immunological knowledge to practical challenges such as rational vaccine design.