Most living things on Earth – from bacteria to humans – must migrate in some way to find favourable conditions. Therefore, they nearly all use chemotaxis, in which their movement is steered by a gradient of chemicals. Chemotaxis is fundamental to many processes that control our well-being, including inflammation, neuronal patterning, wound healing, tumour spread in cancer, even embryogenesis. Understanding it is a key goal for biologists. Despite the fact that many basic principles appear to have been conserved throughout evolution, most research has focused on understanding the molecular mechanisms that control signal processing and locomotion. Cell signaling – cells responding to time-varying external signals – underlies almost all biological processes at the cellular scale. Chemotaxis of single cells provides particularly amenable model systems for quantitative cell signaling studies, even in the presence of noise and fluctuations, because the output, the cell's motility response, is directly observable. However, the different scientific disciplines involved in chemotaxis research rarely overlap, so biologists, physicists and mathematicians interact far too infrequently, methodologies and models differ and commonalities are often overlooked, such as the possible influence of physical or environmental conditions, which has been largely neglected.