The objective of this chapter is to provide suggestions for implementing responsible research and innovation (RRI) in robotics, with a particular focus on Europe, by analysing the role of social aspects, ethics and law in robotics research and development. To what extent can current approaches based on ethical, legal and social aspects of technology (ELSA) be considered to comply with the basic tenets of RRI? How are the often conflictual relationships between social, ethical and legal aspects dealt with in regulating robotics research and applications? The chapter starts by providing a short overview on robotics aimed at making clear its main features and components, in its twofold dimension of research (that is, process) and application (that is, product) and the interaction between these. It also describes the concept of RRI and its relationship with traditional ELSA research. The chapter then moves on to analyse how the social, ethical and legal discourses have entered the field of robotics and how related issues have been addressed by scholars and experts at the European and international levels. This exercise allows us to assess whether and to what extent RRI is embedded in robotics research and applications, in particular in respect of the dimensions of public engagement, research ethics, research integrity and RRI governance. It also allows us to identify the main challenges that robotics research and applications face in an effort towards responsible robotics. These are some of the issues that are discussed in the sections related to society, ethics and law: the role of stakeholders in robotics research and innovation and the relationship between technological innovation, social challenges and techno fixes, as far as social aspects are concerned; integrity in robotics research, and methodologies for identifying and analysing problems and possible solutions, such as ethics by design or machine ethics, concerning ethics. Finally, in relation to these aspects, we assess robotic applications against the backdrop of fundamental values and discuss to what extent these can be embedded in the design of robotic applications. Based on this analysis, we propose suggestions for steering innovation towards enhancing social benefits through regulation aimed at fostering RRI in the robotics development cycle.