[This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.] In recent years, physics instructional labs have been under considerable research and development. However, there seems to be no shared understanding of how the assessment of instructional labs should be arranged to best serve students’ learning and development of expertise. This literature review intends to fill this gap by reviewing the research on classroom assessment of instructional labs from the perspectives of different objectives, purposes, and agents of assessment. The review reveals that classroom assessment in instructional labs has mostly focused on summative assessment, leaving the possibilities of formative assessment understudied. Further, assessment has been conducted mostly by teachers and teaching assistants, and the possibilities for students’ participation in assessment remain unutilized. Two major gaps in the research on instructional labs were identified. The first gap concerns students’ active participation in assessment. Given the active role that students have in the laboratory, their agency in assessment appears to be narrow. The second gap concerns the inclusion of metaskills and perspectives on lifelong learning and work life in assessment. We summarize our findings into a research-based model that assists in the consideration and balancing of different objectives, purposes, and agents in the design of classroom assessment of instructional labs.