Cytotoxic T lymphocytes and natural killer cells eliminate tumor cells or pathogen infected cells. Successful killing comprises several consecutive stages: activation of the killer cell, target search in an inhomogeneous environment, polarization upon target contact, and delivery of the cytotoxic material. In each stage physical processes can be identified that A3 aims to understand in collaboration with other CRC projects. In particular, A3 will focus on the following aspects: 1) Chemotactic search and collective search strategies, 2) T cell migration in synthetic and controllable environments like collagen matrices and obstacle parks, 3) force transmission and mechanical interactions of T cells in collagen matrices, 4) centrosome relocation during formation of the immunological synapse (IS) and actin generated forces at the IS, and 5) killing strategies.