We analyse deep images from the VISTA survey of the Magellanic Clouds in the YJKs filters, covering 14deg^2^ (10 tiles), split into 120 subregions, and comprising the main body and Wing of the Small Magellanic Cloud (SMC). We apply a colour-magnitude diagram reconstruction method that returns their best-fitting star formation rate SFR(t), age-metallicity relation (AMR), distance and mean reddening, together with 68 percent confidence intervals. The distance data can be approximated by a plane tilted in the East-West direction with a mean inclination of 39{deg}, although deviations of up to +/-3kpc suggest a distorted and warped disc. After assigning to every observed star a probability of belonging to a given age-metallicity interval, we build high-resolution population maps. These dramatically reveal the flocculent nature of the young star-forming regions and the nearly smooth features traced by older stellar generations. They document the formation of the SMC Wing at ages <0.2Gyr and the peak of star formation in the SMC Bar at ~40Myr. We clearly detect periods of enhanced star formation at 1.5 and 5Gyr. The former is possibly related to a new feature found in the AMR, which suggests ingestion of metal-poor gas at ages slightly larger than 1Gyr. The latter constitutes a major period of stellar mass formation. We confirm that the SFR(t) was moderately low at even older ages.