Europe faces a crisis. A combination of immigration and differential birthrates is rapidly increasing the proportionate Muslim population at the very time when Muslim/non-Muslim relations are globally strained. Double-edged rejection separates these groups, with mutual fear, distrust, negative feelings and even hatred escalating tensions and distress. It is theoretically plausible that violent jihad against the West may be causally linked to these poor inter-group relations. If so, earnest programs to improve those relations would be expected to reduce the risk of political violence. Sixty years of applied social psychology research has suggested specific interventions that measurably reduce prejudice and improve inter-group relations in the short term. However, there is an astonishing gap in our knowledge: we don't know what works to improve relations in the long-term. This paper summarizes the available evidence and proposes an urgent research agenda to find the optimum ways to improve Muslim/non-Muslim relations in Europe.