Abstract. The ubiquity of smartphones and other location-aware handheld devices has resulted in a dramatic increase in popularity of locationbased services (LBS) tailored to user locations. The comfort of LBS comes with a privacy cost. Various distressing privacy violations caused by sharing sensitive location information with potentially malicious services have highlighted the importance of location privacy research aiming to protect user privacy while interacting with LBS. The anonymity and cloaking-based approaches proposed to address this problem cannot provide stringent privacy guarantees without incurring costly computation and communication overhead. Furthermore, they mostly require a trusted intermediate anonymizer to protect a user’s location information during query processing. In this chapter, we review a set of fundamental approaches based on private information retrieval to process range and k-nearest neighbor queries, the elemental queries used in many Location Based Se...