The Web of Things (WoT) aims at connecting things to applications using web technologies, on top of the Internet of Things. WoT applications are distributed and gather different levels of abstraction. They must be scalable and adapt to dynamic changes in their environment. The question we explore in the scope of my PhD thesis is: how can we deal with context in WoT applications? Our objective is to enable scalable multi-level context-aware adaptation for WoT applications. We intend to build models to describe context and reason about it. First, we have studied related work to identify a set of contextual levels and dimensions and have proposed semantic models suitable for several adaptation tasks in WoT applications. Second, we designed and implemented an architecture that distributes some adaptation tasks onto the client side, to improve reasoning scalability.