Programming by demonstration (PbD) is a key research topic in robotics. It impacts both fundamental research and application-oriented studies.Work in that area tackles the development of robust algorithms for motor control, motor learning, gesture recognition and visuo-motor integration. While the field existed for more than 20 years, recent developments, taking inspiration in biological mechanisms of imitation, have brought a new perspective. Programming by demonstration, now, encompasses more of the learning components of traditional approaches and is often referred to as Learning from Demonstration or Learning by Imitation. This issue aims at assessing the recent progresses in the field, gathering works following either an engineering or a biologically inspired approach.