Telstra is Australia's leading provider of cell phones, mobile devices, home phones and broadband Internet. Save money by buying online. Telstra is Australia's largest telecommunications company, known as Telstra, and is the only state-owned enterprise owned by the Commonwealth of Australia, with a history dating back to 1901. In October 1997, the Australian government partially privatized the company by selling 49.9% of its shares to institutional and individual investors, with the government still holding 50.1% of the shares.