Tourist Trip Design Problems (TTDPs) deal with the task to support tourists in creating a trip composed of a set or sequence of points of interests (POIs) or other items related to travel. This is a challenging problem for personalized recommender systems (RSs), because it is not only needed to discover interesting POIs matching the preferences and interests, but also to combine these destinations to a practical route. In this chapter, we present the TTDP and show how it can be modeled using different mathematical problems. We present trip RSs with a focus on recommendation techniques, data analysis, and user interfaces. Finally, we summarize important current and future challenges that research in the field of tourist trip recommendations faces today. The chapter concludes with a short summary.