Over the last two decades, many small-molecule inhibitors that target kinase signalling have been developed. More than 20 of these inhibitors are FDA (U.S. Food and Drug Administration)-approved and are now being used in the clinics to treat tumours; even more have entered clinical trials. However, resistance to these inhibitors, either intrinsic to the tumour or acquired during treatment, remains a major problem in targeted therapeutics. One of the mechanisms by which tumours become resistant is the rewiring of the signalling networks via feedback, by which the tumour cells re-activate signalling or activate alternative signalling pathways. In the present article, we review insights from recent quantitative signalling studies combining mathematical modelling and experiments that revealed how feedback rewires MAPK (mitogen-activated protein kinase)/PI3K (phosphoinositide 3-kinase) signalling upon treatment and how that affects drug sensitivity.