Making the Internet of Things (IoT) a reality will contribute to extend the context-aware ability of numerous sensitive applications. We can foresee that the context of users will include not only their own spatio-temporal conditions but also those of the things situated in their ambient environment and at the same time, thanks to the IoT, those that are located in other remote spaces. Consequently, next-generation context managers have to interact with the IoT underlying technologies and must, even more than before, address both privacy and quality of context (QoC) requirements. In this article, we show that the notions of privacy and QoC are intimately related and sometimes contradictory and survey the recent works addressing them. Current solutions usually consider only one notion, and very few of them started to bridge privacy and QoC. We identify some of the remaining challenges that next-generation context managers have to deal with to favour users' acceptability by providing both the optimal QoC level and the appropriate privacy protection.