Social robotics is a rapidly developing industry-oriented area of research, intent on making robots in social roles commonplace in the near future. This has led to rising interest in the dynamics as well as ethics of human-robot relationships, described here as a nascent relational turn. A contrast is drawn with the 1990s’ paradigm shift associated with relational-self themes in social psychology. Constructions of the human-robot relationship reproduce the “I-You-Me” dominant model of theorising about the self with biases that (as in social constructionism) consistently accentuate externalist or “interactionist” standpoints as opposed to internalist or “individualistic”. Perspectives classifiable as “ecological relationalism” may compensate for limitations of interactionist-individualistic dimension. Implications for theorising subjectivity are considered.