The COVID-19 pandemic has resulted in a renewed interest in the relationship between public health authorities and the public. Particular attention has been paid to ‘problem publics’ who do not follow health advice. This is not a new issue. As the chapters in this collection demonstrate, the designation of certain groups or populations as problem publics has long been a part of health policy and practice. By exploring the creation and management of these problem publics in a range of time periods and geographical locations, the collection sheds light on what is both specific and particular. For health authorities, publics themselves were often thought to pose problems, because of their behaviour, identity or location. But publics could and did resist this framing. There were, and continue to be, many problems with seeing publics as problems.