Cytotoxic T lymphocytes (CTL) help control virus infections by killing virus-infected (target) cells. How fast do CTL find and kill target cells in vivo? Experiments allow us to follow populations of labeled target cells after their transfer into immune mice where they are killed by CTL. Here, we develop models of the migration and killing processes involved in these experiments and use them to quantitatively analyze the in vivo killing data. These models allow us to estimate the rate constant for killing of target cells by CTL.