Observational learning is referred to as a change in performance following the observation of others. With respect to motor learning, an observed action is known to facilitate motor learning mediated by brain processes that are involved during both, the observation and the execution of a certain task. Observational learning in humans has inspired robotic researchers as it may alleviate the necessity to explicitly program robots or require robots to extensively search for a suitable solution. Further, observational learning may become a central aspect of future hybrid societies where robots closely interact with humans. Here, we summarize the current state of the art in observational motor learning in humans and robots with a focus on upper extremity tasks. Further, we briefly outline a roadmap for better understanding observational motor learning by means of building brain-inspired neuronal models. Bringing together these lines of research not only advances human movement science but, in the long run, may contribute to new programming approaches in robots that facilitate human–robot interaction.