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, going all the way from perception to action and decision. In the same time, research on human-human joint action has become a topic of intense research in cognitive psychology and philosophy, bringing elements and even architecture hints to help our understanding of human-human joint action. In this paper, we would like to analyse some findings from these disciplines and connect them to the human-robot joint action case. This work is for us a first step toward the definition of a framework dedicated to human-robot interaction.