Our smart society strongly relies on data, which are continuously generated, collected, stored, and processed by millions of connected IoT devices and smart sensors. Such data are at the basis of typically complex decision-making processes that require advanced analytics. Due to the vast and increasing amount of data, their storage and processing are often outsourced to third parties (e.g., service providers and decentralized computational services) that might be not fully trustworthy in their operating. In this chapter, we focus on the problem of assessing integrity of query computations involving external service providers, and illustrate possible approaches for enabling the verification of the integrity of query results. We will cover both deterministic approaches, based on the definition of authenticated data structures over the data and giving full integrity guarantees, and probabilistic approaches, based on the insertion of control information in the data and providing probabilistic integrity guarantees.