Digital twins are an important part of the Industry 4.0 idea. They mirror physical goods in the digital world and enhance them with additional capabilities and functions for analysis, forecasting and decisionmaking. This paper contributes to the classification and assessment of Digital Twins using a multidimensional maturity model. The presented method "DT-Assess" enables an application-specific assessment of Digital Twins. The developed maturity model consists of seven categories with a total of 31 characteristics to be evaluated. The systematic evaluation in five application scenarios allows, for the first time, a classification of the respective "digital twin" implementation or concept with the aim of identifying further development options and weaknesses.