Deep learning (DL) systems have gained much popularity in real-world applications. It is therefore important to test and improve the trustworthiness of DL systems, especially for those that are safety- and security-critical. The research on determining the trustworthiness of DL systems remains at an early stage, due to the inherent uncertainty of the systems’ behaviors and outputs. This project aims to develop new techniques for determining the trustworthiness of DL systems, with an emphasis on uncovering and accounting for the underlying uncertainties. The new techniques will address two important problems—the design of oracles for deep neural nets (DNNs) that provide insight about additional properties of the DNNs, and the discrimination between intrinsically imprecise behavior and faulty behavior of systems using DNNs. Using these techniques, we will then develop techniques to support the removal of discovered faults in DL systems and to improve the accuracy and interpretability of the systems.