Abstract Programming by demonstration is an active research field which is predicted to have a large potential for future applications. These include, amongst other fields, the industrial domain (assembly, manufacturing) as well as service robotics. A major challenge consists in devising comprehensive and robust concepts for transferring skills from human to machine. In this presentation, I will talk about imitation learning research at the Honda Research Institute Europe. Starting from our perspective on robot movement representation and control, I will introduce a probabilistic approach towards learning and imitating elementary object movement skills based on kinematic (camera) data. Following this, I will introduce concepts that permit representing forces, and such enable the interaction with the environment. Approaches of this kind employ kinesthetic teaching. This is an intuitive approach to physically guide the robot through a task, whilst recording kinematic and kinetic sensory information. The last part of the talk will cover recent research on learning sequential movement skills. Major challenges in sequential behaviour are posed by learning transitions between consecutive movement primitives, as well as by learning to decide which primitive to activate among a set of possible options. I will show a number of results with different robots, and close with our perspective on future problems and ideas to bring such concepts closer to application.