As parallel to recent advances in space technologies, satellite systems has become a very efficient technique for precise positioning in Geodesy Science. Global Positioning System (GPS) provides X, Y, Z cartesian coordinates and/or phi, lambda, h ellipsoidal latitude, longitude and height with high accuracy to geodetic applications as one of these satellite based techniques. However, the error sources stem from the geometric design of the GPS system and inconsistencies between reference datum of the system and physical reality more or less disturb its performance as a geodetic measurement technique. Today numerous scientific studies are carried on to develop applicable solutions to eliminate or minimize the weakness of this very practical and precise positioning technique. One of the problems, which still could not be solved in many countries, is the height datum inconsistency. Because GPS derived point heights refer to its reference ellipsoid- WGS84. However, in most of the applications such as engineering projects, deformation investigations etc. the heights referenced to geoid are required. To take full advantage of the technique in geodetic practical applications, GPS derived ellipsoidal heights need to be transformed to orthometric heights from geoid (in Turkey). A simple formulation, N = h-H, express the relation between GPS derived heights h and orthometric heights H. In relation, N is called geoid height as the separation of two reference surface (datum). In this paper, specifically, precise local geoid models are emphasized as a solution to serve practical geodetic applications using GPS. The computation techniques and mathematical models are summarized. Also wide spread use of GPS technique with geodetic aims is exemplified. The error sources which affect the measurements and consequently positioning accuracy are mentioned. Finally as the modernization and improvement of satellite based positioning systems, GALILEO - a European Operated Global Navigation Satellite System is mentioned.