The complexity of biological systems, and the explosion of the quantity of biological information which is rapidly becoming available from experimental and clinical studies, necessitate the use of theoretical tools, namely, mathematical and computational modeling. The vertebrate adaptive immune system, with its learning and memory capabilities, is a particularly rich source of modeling challenges. Most difficult within this area is the study of lymphocyte repertoires ? the generation of their diversity and the forces that shape the ever-changing dynamics of lymphocyte clones. I review several examples of problems in lymphocyte repertoire modeling, demonstrate the types of solutions employed, and highlight the contribution of these theoretical studies to immunological research.