With rising demand for indoor location-based services (LBS) such as location-based marketing, mobile navigation, etc., there has been considerable interest in indoor positioning methods as well as their security and privacy. Current survey papers on indoor positioning methods mainly focus on positioning accuracy, whereas discussion on security and privacy considerations is limited. While there are survey papers on the security/privacy of LBS, they mainly focus on the services rather than the positioning methods. On the other hand, various survey papers on Internet of Things security/privacy mostly address device and system security. To fill the gap and complement the aforementioned survey papers, we conduct a systematic and comprehensive survey on indoor positioning security and privacy, focusing on the positioning methods. In particular, we provide the following contributions. First, based on general search (using the systematic PRISMA approach) and specific search, we study related papers published in recent years with the aim of addressing three research questions. Second, to facilitate the survey and study, we categorise the positioning methods into non-collaborative methods (i.e., proximity-based, geometric and fingerprinting methods), collaborative methods (i.e., mobile proximity-based and mobile geometric methods) and others (combining multiple technologies/methods). Third, for each method, we give an overview of the method and discuss its security and privacy issues. Last but not least, we highlight some future research directions and work on indoor positioning security and privacy. In particular, there is a need to conduct more research on collaborative positioning methods, including their security and privacy issues.