Originally introduced by social bookmarking systems, collaborative tagging, or social tagging, has been widely adopted by many web-based systems like wikis, e-commerce platforms, or social networks. Collaborative tagging systems allow users to annotate resources using freely chosen keywords, so called tags . Those tags help users in finding/retrieving resources, discovering new resources, and navigating through the system. The process of tagging resources is laborious. Therefore, most systems support their users by tag recommender components that recommend tags in a personalized way. The Discovery Challenges 2008 and 2009 of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD) tackled the problem of tag recommendations in collaborative tagging systems. Researchers were invited to test their methods in a competition on datasets from the social bookmark and publication sharing system BibSonomy. Moreover, the 2009 challenge included an online task where the recommender systems were integrated into BibSonomy and provided recommendations in real time. In this chapter we review, evaluate and summarize the submissions to the two Discovery Challenges and thus lay the groundwork for continuing research in this area.