The new VISual and Infrared Telescope for Astronomy (VISTA) has started operations in 2009. Over its first five years it collected data for six public surveys, one of which is the near-infrared YJKs VISTA survey of the Magellanic Clouds system (VMC). This survey comprises the Large Magellanic Cloud (LMC), the Small Magellanic Cloud, the Magellanic Bridge connecting the two galaxies and two fields in the Magellanic Stream. The main goals of the VMC survey are the determination of the spatially-resolved star-formation history and the three-dimensional structure of the Magellanic system. The VMC survey is therefore designed to reach stars as faint as the oldest main sequence turn-off point and to constrain the mean magnitude of pulsating variables such as RR Lyrae stars and Cepheids. The VMC data are comprised of multi-epoch observations which are executed following specific time constraints. The first science results, aimed at assessing the scientific quality of the VMC data, include an overview of the distribution of stars in colour-magnitude and colour-colour diagrams, the detection of planetary nebulae and stellar clusters, and the Ks band light-curves of variable stars. The VMC survey represents a tremendous improvement, in spatial resolution and sensitivity, on previous panoramic observations of the Magellanic system in the near-infrared, providing a powerful complement to deep observations at other wavelengths.