We present a mission designed to address two main themes of the ES A Cosmic Vision Programme: the Evolution of the Universe and its Violent phenomena. ESTREMO/WFXRT is based on innovative instrumental and observational approaches, out of the mainstream of observatories of progressively increasing area, i.e.: Observing with fast reaction transient sources, like GRB, at their brightest levels, thus allowing high resolution spectroscopy. Observing and surveying through a X-ray telescope with a wide field of view and with high sensitivity extended sources, like cluster and Warm Hot Intragalactic Medium (WHIM). ESTREMO/WFXRT will rely on two cosmological probes: GRB and large scale X-ray structures. This will allow measurements of the dark energy, of the missing baryon mass in the local universe, thought to be mostly residing in outskirts of clusters and in hot filaments (WHIM) accreting onto dark matter structures, the detection of first objects in the dark Universe, the history of metal formation. The key asset of ESTREMO/WFXRT with regard to the study of Violent Universe is the capability to observe the most extreme objects of the Universe during their bursting phases. The large flux achieved in this phase allows unprecedented measurements with high resolution spectroscopy. The mission is based on a wide field X-ray/hard X-ray monitor, covering >l/4 of the sky, to localize transients; fast (min) autonomous follow-up with X-ray telescope (2000 cm2) equipped with high resolution spectroscopy transition edge (TES) microcalorimeters (2eV resolution below 2 keV) and with a wide field (1°) for imaging with 10" resolution (CCD) extended faint structures and for cluster surveys. A low background is achieved by a 600 km equatorial orbit. The performances of the mission on GRB and their use as cosmological beacons are presented and discussed.