The Wide Field X-ray Telescope (WFXT) is a proposed mission with a high survey speed, due to the combination of large field of view (FOV) and effective area, i.e. grasp, and sharp PSF across the whole FOV. These characteristics make it suitable to detect a large number of variable and transient X-ray sources during its operating lifetime. Here we present estimates of the WFXT capabilities in the time domain, allowing to study the variability of thousand of AGNs with significant detail, as well as to constrain the rates and properties of hundreds of distant, faint and/or rare objects such as X-ray Flashes/faint GRBs, Tidal Disruption Events, ULXs, Type-I bursts etc. The planned WFXT extragalactic surveys will thus allow to trace variable and transient X-ray populations over large cosmological volumes. ; Comment: Proceedings of "The Wide Field X-ray Telescope Workshop", held in Bologna, Italy, Nov. 25-26 2009 (arXiv:1010.5889). To appear in Memorie della Società Astronomica Italiana 2010 - Minor corrections to text-