Up to a few years ago, the typical robot was a dangerous and powerful machine, used in confined areas to execute dangerous and repetitive tasks (e.g., welding together the different parts composing the car body). Recently, robots have evolved into something radically different: intelligent robots (IR). IRs are lightweight and agile machines endowed with sufficient computing power to execute autonomous tasks in human-populated areas. This new generation of machines can directly collaborate with humans in the execution of their work, provide support and relief to weak users (e.g., older adults with physical and cognitive deficits) and transport goods and even people between different locations in the environment. To operate properly, IR need adequate motion planning algorithms that satisfy the necessary safety constraints and exhibit socially acceptable behaviours. When we meet other people in a public space, we do not treat them as moving obstacles: we anticipate their choice, establish non-verbal communication protocols and use the shared space in safe and efficient ways. For years, the holy grail of robotic research on human-aware motion planning has been to seek solutions that could replicate, at least in part, some of these complex behavioural patterns. In this talk, we will review some of the results of the IDRA group in this area focusing on three different sub-problems: 1. predict the motion of the humans in the scene, 2. integrate this prediction into motion planning algorithms to generate smooth and socially acceptable motions, 3. account for the psychological interaction whereby humans and robots can influence each other’s decision to produce a desired behaviour.