Smart IoT systems can integrate knowledge from the surrounding environment, and they are critical components of the next-generation Internet. Such systems usually collect data from various dimensions via numerous devices, and the collected data are usually linkable. This means that they can be combined to derive abundant valuable knowledge. However, the collected data may also be accessed by malicious third parties to reveal sensitive information. In this article, we investigate the privacy issues of linkable data in smart IoT systems, which have not been thoroughly studied in previous works. We first discuss the available data sources in smart IoT systems and their linkage. Then we introduce some third parties who may access and utilize the linkable data. The potential threats are comprehensively elaborated for both individuals and crowds in smart IoT systems. Finally, we highlight some challenges and open problems for privacy preservation of linkable data in smart IoT systems.