As the field of digital preservation matures, there is an increasing need to systematically assess an organization's abilities to achieve its digital preservation goals, and a wide variety of assessment tools have been created for this purpose. To map the landscape of research in this area, evaluate the current maturity of knowledge on this central question in DP and provide direction for future research, this paper reviews assessment frameworks in digital preservation through a systematic literature search and categorizes the literature by type of research. The analysis shows that publication output around assessment in digital preservation has increased markedly over time, but most existing work focuses on developing new models rather than rigorous evaluation and validation of existing frameworks. Significant gaps are present in the application of robust conceptual foundations and design methods, and in the level of empirical evidence available to enable the evaluation and validation of assessment models. The analysis and comparison with other fields suggest that the design of assessment models in DP should be studied rigorously in both theory and practice, and that the development of future models will benefit from applying existing methods, processes, and principles for model design.