This paper examines a question posed in 2019 in the "International Journal on Training and Development": 'How do we solve a problem like apprenticeship?' Data sources covering a substantial number of countries are used to present findings on, and analyse, initiatives that have been implemented or that have been considered, and then to develop some analytical constructs to help address the question. Fundamental issues such as the status of vocational education and training and the status of apprenticed occupations are important, but the nature of the apprenticeship arrangements, within countries and within industries are also major factors affecting perceived attractiveness. The paper therefore argues that the heterogeneity of apprenticeship systems and arrangements is a major barrier to solving the attractiveness problem. Moreover, the heterogeneity of potential apprenticeship applicants means that marketing campaigns or other efforts to attract more, and higher quality, apprentices need to be cognisant of individuals' backgrounds, characteristics, and aspirations. Some tentative ways of addressing these matters are presented, but the conclusion is that the topic needs large-scale research.