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Many sensor applications are being developed that require the location of wireless devices, and localization schemes have been developed to meet this need. However, as location-based services become more prevalent, the localization infrastructure will become the target of malicious attacks. These attacks will not be conventional security threats, but rather threats that adversely affect the ability of localization schemes to provide trustworthy location information. This paper identifies a list of attacks that are unique to localization algorithms. Since these attacks are diverse in nature, and there may be many unforeseen attacks that can bypass traditional security countermeasures, it is desirable to alter the underlying localization algorithms to be robust to intentionally corrupted measurements. In this paper, we develop robust statistical methods to make localization attack-tolerant. We examine two broad classes of localization: triangulation and RF-based fingerprinting methods. For triangulation-based localization, we propose an adaptive least squares and least median squares position estimator that has the computational advantages of least squares in the absence of attacks and is capable of switching to a robust mode when being attacked. We introduce robustness to fingerprinting localization through the use of a median-based distance metric. Finally, we evaluate our robust localization schemes under different threat conditions.