The mental attitudes of belief, desire, and intention play a central role in the design and implementation of autonomous agents. In 1987 Bratman proposed their integration into a belief-desire-intention (BDI) theory that was seminal in AI. Since then numerous approaches were built on the BDI paradigm, both practical (BDI architectures and BDI agents) and formal (BDI logics). The logical approaches that were most influential are due to Cohen&Levesque and to Rao&Georgeff. However, three fundamental problems remain up to now. First, the practical and the formal approaches evolved separately and neither fertilized the other. Second, only few formal approaches addressed some important issues such as the revision of intentions or the fundamentally paraconsistent nature of desires, and it seems fair to say that there is currently no consensual logical account of intentions. Finally, only few publications study the interaction between intention and other concepts that are naturally connected to intention, such as actions, planning, and the revision of beliefs and intentions. Our paper summarizes the state of the art, discusses the main open problems, and sketches how they can be addressed. We argue in particular that research on intention should be better connected to fields such as reasoning about actions, automated planning, and belief revision and update.