The Magellanic Clouds (MCs) are the Milky Way's most massive dwarf satellites. As they also represent the closest pair of galaxies in an ongoing tidal interaction, while simultaneously infalling into the Milky Way halo, they provide a unique opportunity to study in detail an ongoing three-body encounter. We present the "YMCA (Yes, Magellanic Clouds Again) survey: probing the outer regions of the Magellanic system with VST" based on deep optical photometry carried out with the VLT Survey Telescope (VST). YMCA targeted 110 square degrees, in the g and i filters, in the periphery of both the MCs, including a long strip in between the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). The photometry of YMCA is sufficiently deep (50% complete down to g=~23.5-24.0mag) to allow for a detailed analysis of main-sequence stars in regions of the MCs remained relatively unexplored at these faint magnitudes. The resulting colour-magnitude diagrams reveal that the outskirts of the MCs are predominantly characterized by intermediate-age and old stellar populations, with limited or negligible evidence of recent star formation. The analysis of the age distribution of star clusters (SCs) within the surveyed area, both already known and newly discovered candidates, hints at a close fly-by between the LMC and SMC that occurred =~2.5-3.0Gyr ago, in agreement with previous results. We also report the discovery of candidate SCs with ages within the so-called "age-gap", questioning its real existence.