The offering of anonymity in relational databases has attracted a great deal of attention in the database community during the last decade . Among the different solution approaches that have been proposed to tackle this problem, K-anonymity has received increased attention and has been extensively studied in various forms. New forms of data that come into existence, like location data capturing user movement, pave the way for the offering of cutting edge services such as the prevailing Location Based Services (LBSs). Given that these services assume an in-depth knowledge of the mobile users' whereabouts it is certain that the assumed knowledge may breach the privacy of the users. Thus, concrete approaches are necessary to preserve the anonymity of the mobile users when requesting LBSs. In this work, we survey recent advancements for the offering of K-anonymity in LBSs. Most of the approaches that have been proposed heavily depend on a trusted server component -- that acts as an intermediate between the end user and the service provider - to preserve the anonymity of the former entity. Existing approaches are partitioned in three categories: (a) historical K-anonymity, (b) location K-anonymity, and (c) trajectory K-anonymity. In each of these categories we present some of the most prevalentmethodologies that have been proposed and highlight their operation.