Wu deposed Empress Wang by rousing suspicion that the Empress had murdered Wu's infant daughter. The exact circumstances of this situation are disputed and unclear. Some have suggested that Wu killed her own daughter to frame the Empress. Another theory is that the infant died of unrelated causes and Wu used it as an opportunity to attack the Empress. Whatever the truth, Wu Zhao became the new wife of Emperor Kao Tsung.
Within a few years, Kao Tsung suffered a stroke, abruptly ending his reign. Wu started making moves. She established her youngest and weakest son as the new Emperor and began to control China through him. Her Secret Police started spiriting away her opponents, and she commissioned scholars to challenge the traditional status of women in Confucian doctrine. In other words, Wu Zhao was starting to act like someone trying to become the Emperor of China.
In the year 690, Wu Zhao's son stepped down from the position of Emperor, and in his place, she became Wu Zetian, Emperor of China. After years of ruthless backstabbing political maneuvering, Wu Zetian started initiating positive social reform. She reduced taxation, improved public utilities and development, and began phasing out militaristic aristocrats in favor of scholars. Emperor Wu Zetian established the Second Zhou Dynasty, and as its first ruler, reigned from 690 to 705 AD.
I'd like to highlight something about Wu's status. Traditionally in Imperial China, the Emperor's wife was the "Empress Dowager", and would be granted certain provisional governance in the Emperor's wake. The Chinese word for this position was Huanghou. Wu Zetian did not take this title. Empress Wu was called Huangdi, the title of the Emperor.
In English, the distinction seems minor, but in Chinese, the difference is massive. An Empress Dowager was, by divine establishment, lesser than the Emperor. Wu Zetian was not The Empress Dowager, she was The Emperor of China. In establishing the second Zhou Dynasty, Wu Zetian became the only woman ever to be Huangdi. (In bold because that's a pretty big goddamn deal in this context).
Wu Zetian believed she was descended from the founders of the first Zhou Dynasty, which, interestingly enough, was the dynasty that established The Mandate of Heaven.
The Mandate of Heaven dictates that the will of Heaven itself is what upholds the power of China's ruler. A just, noble, and strong leader is maintained by the Mandate, and will prosper. An immoral ruler will be diminished by the Mandate. Famine, poverty, and weakness were signs that an Emperor had lost the Mandate of Heaven.
There have been disputes, both inside and outside China, as to whether Wu Zetian's status as Emperor was legitimate. As of the time of writing this, however, it is generally accepted among historians that Wu Zetian was indeed an Emperor of China. It is my belief that Wu Zetian's success in Imperial Chinese politics both before and during her reign as Emperor firmly establishes her legitimacy under the standards of the Mandate of Heaven.