abstract: An important part of the body's immune response is the encounter between T cells and antigen- presenting cells inside lymph nodes, where their motion appears to be random. I will discuss ways to estimate timescales under the simplest hypothesis, that cell motion is Brownian. I will also consider homeostasis: a repertoire of T cells of many dierent specicities is maintained over many years because death of cells is balanced by a combination of cell division and new cells from the thymus. Our knowledge is based on estimates and extrapolation from small samples.