It is a well-recognized fact that a Cyber-Physical System (CPS) experiences uncertain (including unknown) situations during their operations. Some of such uncertainties could potentially lead to failures of CPS operations. Factors contribute to such uncertainties include 1) the intrinsically unpredictable physical environment of a CPS, 2) the use of communication networks continuously experiencing problems (e.g., slower connection than expected), and 3) the increasing use of machine learning algorithms in CPSs which introduce inherent uncertainties to these CPSs. No matter how meticulously a CPS is designed and developed, it is impossible to predict all possible uncertain situations it will experience during its operation. Thus, there is a need for new methods for discovering and handling uncertain situations during the CPS operation to prevent it from failure. In this paper, we present our ideas on how digital twins, i.e., "live models" of CPSs can help in discovering and handling potentially unsafe situations during its operation. We present the research challenges and potential solutions to develop, deploy, and operate such digital twins. The presented work is planned to be performed in a recently accepted European research-based innovation project, ADEPTNESS.