For more than a decade, the field of human-robot interaction has generated many valuable contributions of interest to the robotics community at large. The field is vast and addresses issues in perception, decision, action, communication and learning, as well as their integration. At the same time, research on human-human joint action has become a topic of intense research in cognitive psychology and philosophy, providing elements and even offering architecture hints to help our understanding of human-human joint action. In this paper, we analyse some findings from these disciplines and connect them to the human-robot joint action case. This work is a first step toward the development of a framework for human-robot interaction grounded in human-human interaction.