Named after joint Nobel Prize recipients, Sir William Bragg and his son Sir Lawrence Bragg, the seat has been held by Liberal Members since its creation in 1970.

The Bragg electorate currently includes the following suburbs: Auldana, Beaumont, Beulah Park, Burnside, Cleland, Erindale, Greenhill, Glen Osmond (portion), Hazelwood Park, Horsnell Gully, Heathpool, Kensington, Kensington Park, Kensington Gardens, Leawood Gardens, Leabrook, Linden Park, Mount Osmond, Marryatville, Rosslyn Park, St Georges, Stonyfell, Skye, Toorak Gardens, Tusmore, Wattle Park and Waterfall Gully.

In a recent SA Electoral Boundary Redistribution report, the seat of Bragg will change after the next election in March 2022. For this election, the suburbs who will be voting in Bragg include:  Beaumont, Burnside, Cleland, Dulwich, Eastwood, Erindale, Frewville, Glen Osmond, Glenside, Glenunga, Greenhill, Hazelwood Park, Horsnell Gully, Heathpool, Leawood Gardens, Leabrook, Linden Park, Mount Osmond, Marryatville, Rose Park, Rosslyn Park, St Georges, Stonyfell, Skye, Toorak Gardens, Tusmore, Wattle Park and Waterfall Gully.

Former Premier David Tonkin (1970-83), former Deputy Premier Graham Ingerson (1983-02), and current Deputy State Liberal Leader Vickie Chapman (2002-present) have represented local constituents in the South Australian Parliament.