Title:Velocity dispersion profiles of globular clusters: a mirror of tidal effects, modified gravity and structural evolution Abstract: I present the recent developments in the analysis of the velocity dispersion profiles of Galactic globular clusters in the light of the growing body of observational data and theoretical modelling. In particular, extensive spectroscopic surveys performed on the giant globular cluster omega Centauri and in the outermost globulars (populating the outer halo of the Milky Way) have been used to test the effects of the tidal interaction of these stellar systems with the Milky Way potential as well as the fundamental law of gravity. I will show that the comparison with suitable theoretical models and N-body simulations provides important clues and constraints on the orbit and structural evolution of these objects and on the validity of alternative gravitation theories.