The Web of Things (WoT) promises to dramatically boost the potentiality of interconnecting smart and physical devices over the Internet as it not only enhances ergonomics and productivity of the Internet of Things (IoT), but it also introduces new capabilities for device interoperation and data aggregation and analysis. These advances pose the challenge of preserving data security and privacy (S&P), as well as the reliability of the overall infrastructure. Deploying existing S&P solutions and technologies in the WoT is not straightforward because of its potential vastness, its intrinsic inhomogeneity and the wide variety of involved entities and interests. In such scenario, every choice comes from a non-trivial trade-off among different aspects including security, availability and legal issues. In this paper, we investigate the nature of this trade-off, pointingout the different kinds of S&P issues and surveying some of the available solutions. In addition, we discuss the major issues raised while securing an existing WoT infrastructure.