The environment plays a major role in shaping galaxy evolution. Galaxies located in high density regions have physical properties in terms of morphology, gas content, and star formation significantly different than those of their counterparts in the field. In rich environments their evolution can be perturbed by different mechanisms, those related to the gravitational interaction with other members or with the potential well of the structure itself, and hydrodynamic with the hot and dense intergalactic medium. I will introduce the VESTIGE survey, a blind, narrow-band Halpha imaging survey carried out with MegaCam at the CFHT (2017-2021 French-Canadian Large Program) to map the whole Virgo cluster region up to one virial radius. Given its proximity (16.5 Mpc) and the access to a unique set of multifrequency data, the Virgo cluster is the ideal laboratory for understanding the relative contribution of gravitational and hydrodynamic perturbations in modyfing galaxy evolution in rich environments. This survey has been designed to study at an unprecedented sensitivity (SHa ~ 2 x 10^-18 erg sec^-1 cm^-2 arcsec^-2) and angular resolution (< 1 arcsec) the effects of the environment on cluster galaxies through the observation of the ionised gas component, ideal tracer of an ongoing perturbation. I will summarise the first results obtained so far based on the analysis of the core of the cluster and of some representative objects undergoing different kind of perturbations.