Understanding is used in educational contexts and assessment often without further explanation, assuming that the meaning is self-evident and shared by students, teachers and researchers of learning alike. On a daily basis however, teachers are confronted with differences in how students interpret understanding affecting what and how they learn and know. Conversely, teachers’ own interpretation of understanding shapes their teaching and so how students learn (for an overview see van Rossum & Hamer 2010). Lack of awareness of the existing range of conceptions of understanding and how these may undermine effective learning, teaching and valid assessment of learning should be a concern, but seldom seems to be. The current mainstream of research on understanding points appears to have not progressed beyond understanding as flexible performance as used within the Teaching for Understanding approach developed within Project Zero (Perkins, 1993). The learners´ focus on study success makes assessment a potentially powerful tool to influence learning especially if assessment is geared towards awarding credit for deep understanding. The current paper presents a short review of the literature on conceptions of understanding up to 2015, linking it to epistemological models (e.g. Kegan, 1994) and providing an overview of twelve possible indicators to guide further research into more complex ways of understanding (e.g. Entwistle & Peterson, 2004; Kegan, 1994). These indicators include the return of emotion in learning and deep understanding, connectedness and coherence, flexible adaptation to unknown situations, paradoxical thinking, alertness and open mindedness and identity development. It presents empirical qualitative data (N=167) supporting the recognition of at least two more complex ways of understanding that undergraduate students in higher education entertain, namely understanding-in-relativity and understanding-in-supercomplexity (Hamer & Van Rossum, 2016), as well as how students think such more complex understanding may be assessed. In the data students further discuss their views on existing assessment methods and their validity and success regarding assessing deep understanding, directly linking assessment methods to learning strategies and motivation to study. It proposes the development of two matching approaches to curriculum development and aligned assessment based on the constructive alignment approach (Biggs, 2003), relativist alignment to encourage understanding-in-relativity and inner-alignment supporting the development of understanding-in-supercomplexity (Hamer & van Rossum, 2016).