AI technologies, including deep learning, large-language models have gone from one breakthrough to the other. As a result, we are witnessing growing excitement in robotics at the prospect of leveraging the potential of AI to tackle some of the outstanding barriers to the full deployment of robots in our daily lives. However, action and sensing in the physical world pose greater and different challenges than analysing data in isolation. As the development and application of AI in robotic products advances, it is important to reflect on which technologies, among the vast array of network architectures and learning models now available in the AI field, are most likely to be successfully applied to robots; how they can be adapted to specific robot designs, tasks, environments; which challenges must be overcome. This article offers an assessment of what AI for robotics has achieved since the 1990s and proposes a short- and medium-term research roadmap listing challenges and promises. These range from keeping up-to-date large datasets, representatives of a diversity of tasks robots may have to perform, and of environments they may encounter, to designing AI algorithms tailored specifically to robotics problems but generic enough to apply to a wide range of applications and transfer easily to a variety of robotic platforms. For robots to collaborate effectively with humans, they must predict human behavior without relying on bias-based profiling. Explainability and transparency in AI-driven robot control are not optional but essential for building trust, preventing misuse, and attributing responsibility in accidents. We close on what we view as the primary long-term challenges, that is, to design robots capable of lifelong learning, while guaranteeing safe deployment and usage, and sustainable computational costs.