Sport directly or indirectly affects the lives of millions of people around the world. For professional federations, the quality of the schedules strongly affects their financial turnover (media revenue, sales at stadiums, ticket sales etc.). For non-professional tournaments, it affects the distribution of games, tournament length, travelling distances, associated costs etc. Scheduling sport competitions is a hard combinatorial optimisation problem, studied at length by researchers, at least for some problem variants. In this position paper, we argue that there are still several challenges in this field that are worthy of attention. On one side, ‘traditional’ sport scheduling problems (SSPs) still present open research questions that should be investigated. On the other, we argue that there has been a skewed focus towards the SSPs of interest for professional sport federations, while other SSPs have received less attention despite their theoretical and practical interest.