This chapter reports the results of three research studies on peer assessment carried out in different countries where it is an unusual practice (France, Switzerland, and the Czech Republic). The three research studies focus on different competences and different disciplines (sciences and mathematics), but they all involve inquiry-based approaches at primary and secondary school level. In the French study, the data reported in this chapter explore relationships between success in task processing and the ability to mark a peer’s written artefact on the same task. The Swiss research study examines the type of peer feedback students offer their peers while assessing their models, based on a fine-grained analysis of peer feedback comments. In the Czech Republic, the study focuses on students’ reflection on peer assessment in inquiry lessons. The three studies conclude the necessity of allowing the sharing of “knowledge authority” in the classroom to evolve and to be integrated into usual classroom practice. However, researchers have a divergent view on the sharing of responsibility for validation of knowledge between the student and the teacher. Moreover, we can conclude that peer assessment can be a way to trigger metacognitive work on knowledge and competences in science and on assessment criteria and teacher expectations, at a class level and individual student level.