Background Governments can intervene to change health-related behaviours using various measures but are sensitive to public attitudes towards such interventions. This review describes public attitudes towards a range of policy interventions aimed at changing tobacco and alcohol use, diet, and physical activity, and the extent to which these attitudes vary with characteristics of (a) the targeted behaviour (b) the intervention and (c) the respondents. Methods We searched electronic databases and conducted a narrative synthesis of empirical studies that reported public attitudes in Europe, North America, Australia and New Zealand towards interventions relating to tobacco, alcohol, diet and physical activity. Two hundred studies met the inclusion criteria. Results Over half the studies (105/200, 53%) were conducted in North America, with the most common interventions relating to tobacco control (110/200, 55%), followed by alcohol (42/200, 21%), diet-related interventions (18/200, 9%), interventions targeting both diet and physical activity (18/200, 9%), and physical activity alone (3/200, 2%). Most studies used survey-based methods (160/200, 80%), and only ten used experimental designs. Acceptability varied as a function of: (a) the targeted behaviour, with more support observed for smoking-related interventions; (b) the type of intervention, with less intrusive interventions, those already implemented, and those targeting children and young people attracting most support; and (c) the characteristics of respondents, with support being highest in those not engaging in the targeted behaviour, and with women and older respondents being more likely to endorse more restrictive measures. Conclusions Public acceptability of government interventions to change behaviour is greatest for the least intrusive interventions, which are often the least effective, and for interventions targeting the behaviour of others, rather than the respondent him or herself. Experimental studies are needed to assess how the presentation of the problem and the benefits of intervention might increase acceptability for those interventions which are more effective but currently less acceptable.