Across the world, teachers' classroom assessment tasks and responsibilities are becoming more diverse due to increased migration. In this review, we address how migrant students are affected by assessment, both summative and formative, at the classroom level, with a focus on culturally responsive assessment (CRA). Previous research has shown that CRA practices mainly occur in student-centred classrooms. Furthermore, both student and teacher beliefs about teaching and learning might negatively affect migrant students' opportunities to engage in assessment situations. Teaching and assessment practices should be negotiated and aligned with and included in classroom norms to be culturally responsive. We propose that what is generally considered a valid and reliable assessment practice might need to be adjusted to account for students' cultural ways of knowing and participating and how this is expressed and communicated within the classroom.