Interferometry in the visible now provides milliarcsecond spatial resolution and thus has been intensely used for studying the circumstellar environment of evolved and pre-sequence stars. Up to now, most of the scientific results were obtained using only the modulus of the visibility as a function of baseline, time or projected baseline (the so-called "super-synthesis" effect). In this paper we will try to show that even without images, the phase of the visibility is able to put very strong constraints on stellar modeling since it is possible to achieve μarsecond measurements using this technique. We will illustrate through two examples from the GI2T interferometer how the modulus and the phase of the visibility were used to understand the physics of Be disks. We will stress on the importance and the potential of coupling high angular resolution with high spectral resolution for the study of stellar physics. Finally, We will present a possible study on the phase signatures due to stellar rapid rotation that can be done using the VLTI interferometer.