This paper focuses on peer feedback in relation to assessment processes. It examines the rationale for peer feedback, emphasizing its potential for enhanced student learning. We draw on relevant literature to argue that the dominance of peer assessment processes using grades can undermine the potential of peer feedback for improving student learning. The paper throws further light on the issue by drawing on a large-scale questionnaire survey of tertiary students (1740) and academics (460) in Hong Kong, supplemented by interview data. The findings indicate that a significant number of academics and students resist peer assessment using grades and that the majority report that students never or rarely grade each other in assessment activities. This paper explores why there is resistance, in particular, by academics to peer assessment and argues the case for a peer feedback process as an end in itself or as a precursor to peer assessment involving the awarding of marks. It also recommends some strategies for promoting peer feedback, through engaging students with criteria and for embedding peer involvement within normal course processes. (Contains 2 tables.)