Given the success of high-altitude wide-field gamma-ray detectors in the northern hemisphere, such as HAWC and LHAASO, a similar observatory in the TeV-PeV energy range is desirable in the southern hemisphere. The proposed Southern Wide-field Gamma-ray Observatory (SWGO), currently in the R&D phase, will be a ground-based, high duty cycle, extensive air shower water Cherenkov detector array with a high fill factor core. The detector is expected to be located in the Atacama Astronomical Park, Chile, at an altitude of 4770 m, with strong participation from Latin American institutions. SWGO will allow monitoring of the Galactic Centre, a large part of the Galactic plane and the southern Fermi bubble, as well as providing full sky coverage for transient (e.g. GRBs) and variable multi-wavelength phenomena, opening the window to new PeV sources and complementing the observations of the Cherenkov telescope array. In this talk, I will discuss the science goals, array design options, prototype detector units, and performance expectations. I will also give an overview of the project activities in terms of current status and schedule.