Livia married Augustus after divorcing her first husband who was on the losing side of a war against Augustus, but was spared during a general amnesty. Her first husband was even at her wedding in 38 B.C. She and Augustus remained married until his death in 14 A.D. and as he became the first Emperor of Rome, she wielded considerable authority.
Ancient Roman historians cast a mixed picture of Livia, viewing her as paragon of the dutiful wife in public and great assistant to her husband in his governing of the Empire, but coniving in making sure nothing would stand in the way of making sure her line, the Claudians, succeeded to the Emperorship after Augustus' death. She is blamed with orchestrating a number of deaths and banishments, and, indeed, it does seem the line of Augustus ran into more than its fair share of hardships to clear the way for Tiberius to take the thrown.
Her relationship with her son soured however once he became Emperor, so much so that he was not even present at her death, even though there was ample warning of failing health. Furthermore when the senate voted her the status of godhood such as was granted to Augustus, Tiberius forbid it and would not allow it. Livia was declared a goddess, but not until Claudius became emperor.