Student assessment is integral to curriculum design and to the learning journey of all students. Assessment is about process and outcomes. It enables a learner to determine their progress through the medium of ongoing feedback, and it also determines whether a student has met the intended learning outcomes. The focus on assessment in higher education is increasing, being closely linked to the enhancement of learning and teaching strategies and the emphasis on student-centred learning. There is political and institutional high-level commitment to promoting an assessment design which is holistic and based on co-creation between students and academic staff. Core practices in student assessment often remain problematic, and teachers and institutions face diverse challenges in using research to improve assessment and feedback practices. Crucial challenges include approaches which take into consideration increasingly diverse student cohorts, ensuring the integrity of assessment, and being mindful of the workload for both teachers and students. The EUA Thematic Peer Group "Student assessment", composed of academics, institutional management and students, was invited to examine how student learning can be assessed in a way that takes into account both qualitative indicators and pedagogical progress, including peer and self-assessment, and caters for students' individual needs. This report is the product of the discussions and conclusions of the group. The report aims to encourage further reflections and conversations around student assessment, and to provide tools to support development of assessment feedback at the institutional level.