The tracking of the orbit of a star around SgrA* is one of the most beautiful achievements of astronomy. It is the focus of this chapter. This measurement has led to the most convincing evidence for the existence of a supermassive black hole and to an accurate measurement of its mass. In addition, this is also a simple example of the general dynamical paradigm used to determine whether a system contains some form of invisible matter coexisting with the visible matter. Here, the invisible matter (a black hole) has nothing to do with the concept of dark matter as is commonly envisaged in modern astrophysics. After a section on the dynamical paradigm that leads to declare a discrepancy between mass present and visible mass, some observations are recalled that for decades have suggested that our Galaxy should host a central supermassive black hole. Then the main characteristics of the more recent study of star orbits close to the source SgrA* are described, with additional comments on the detection of supermassive central black holes in other galaxies. The final dynamical section is devoted to some general concepts about orbits; it also includes a short description of quasi-circular star orbits in spherical or axisymmetric time-independent potentials.