With the increasing popularity of peer assessment as an assessment tool, questions may arise about its measurement quality. Among such questions, the extent peer assessment practices adhere to standards of measurement. It has been claimed that new forms of assessment, require new criteria to judge their validity and reliability, since they aim for specific goals and address different aspects of learning. But although new criteria have been formulated, little is known about how they are deployed and operate in actual peer assessment practices. This study intends to explicate the quality criteria relevant to the context of peer assessment. We conducted a survey in vocational education on peer assessment quality criteria applied in classrooms. Fifty-six teachers using peer assessment rated several quality criteria as relevant to their teaching practice. The findings suggest that peer assessment practices entail many of the quality criteria recognized in measurement and evaluation, although in an embedded way: the generic quality criteria are tuned or adapted to the peer assessment setting. The findings also show that peer assessment is very much in the hands of the teacher, who organizes and orchestrates the appraisal process in which students receive clear guidelines to appraise one another's work. Our results indicate that quality criteria hardly differ from the function peer assessment serves in classrooms, either within a summative or formative evaluation context. By gaining insight on the specific criteria of peer assessment and their precise purposes, we believe it becomes possible to help teachers improve its measurement quality.