The Sustainable Development Goals (SDGs) adopted by the United Nations for the period 2016-2030 aim to achieve a substantial reduction of interpersonal violence. An increasing body of evidence of what works, emerging from randomized controlled trials, can inform public health policy decisions. However, there is very limited evidence on the kinds of mechanisms that lead to sustained declines in interpersonal violence at the population level. We discuss the implications of what is known about recent major declines in violence to guide violence-reduction policies.