Over the last couple of years the "Dynamical Systems and Robotics" group at the University of Minho has developed and experimentally validated the dynamic approach to Cognition and Robotics. In my talk I give an overview about the approach with a focus on mathematical challenges, on the link to experimental data in the Cognitive Sciences, and on validation results in human-robot interaction studies. Specific problems will be addressed in more detail in a series of subsequent talks.