The repertoire of antigen-specific receptors expressed by our B and T cells contains a record of our immune history, and encodes defences against future challenges. How to decode this information from repertoire sequencing remains an open challenge. I will show how computational methods and theories of immune response and memory can help us make progress. I will also present some modeling efforts to understand how our immune systems shape and are shaped by the evolution of circulating viruses in a continual process of co-evolution.