The Vista Variables in the Via Lactea (VVV) ESO Public Survey consists in a near-infrared time-series survey of the Galactic bulge and inner disk, covering 562 square degrees of the sky, over a total timespan of more than 5 years. In this paper, we provide an updated account of the current status of the survey, especially in the context of stellar variability studies. In this sense, we give a first description of our efforts towards the construction of the VVV Variable Star Catalog (VVV-VSC).