While the current ground-based gamma-ray instruments HAWC, ARGO, and LHAASO, are successfully exploring the large-scale Northern hemisphere at the very-high energies, no such observatory exists in the Southern hemisphere. The proposed next-generation gamma-ray survey observatory SWGO will disclose the full Southern hemisphere for the first time up to hundreds of TeV. SWGO will allow mapping the Galactic large scale emission, and will provide access to the Galactic center and to the full-sky for transients and variable multi messenger phenomena. It will probe anisotropies and the sources of high-energy cosmic rays. With its wide field of view and its deep sensitivity, even at the highest energies, SWGO will allow observations of a large number of steady and transient sources simultaneously, including diffuse sources and large scale structures, unveiling their details and morphologies. SWGO concept is the nowadays missing observatory for multi-frequency and multi-messenger studies. In the current R&D phase, we present, on behalf of the well-established international consortium (www.swgo.org), the SWGO concept with its science case and perspectives.