We will describe the current status of the ASTRI Mini-Array, under construction at the Teide Astronomical Observatory in Tenerife, Spain. The final layout of the array will include nine small Cherenkov telescopes covering an area of about 650 x 270 square meters. The ASTRI telescopes adopt a dual-mirror Schwarzchild-Couder aplanatic optical design. In the focal plane, the ASTRI camera, based on silicon photo-multiplier detectors, will cover a large field-of-view ( > 10 deg in diameter). This system also provides good gamma-ray sensitivity at very high energies (VHE, above 10 TeV) combined with a good angular resolution. The scientific goals of the ASTRI Mini-Array include spectral and morphological characterization of the LHAASO sources and other Pevatron candidates, studies of PWNe and TeV halos, Blazar monitoring at VHE, fundamental physics and follow-up of transient events. The beginning of the scientific operations is planned for mid 2025. The first three years will be dedicated to the core science and the ASTRI Mini-Array will be run as an experiment. It will gradually move towards an observatory model in the following years, open to the community.