The first prototypes of innovative very wide field X-ray telescopes of Lobster-Eye type confirm the feasibility to develop such instruments for flight in the near future. These devices are expected to allow very wide field (more than 1000 square degrees) monitoring of the sky in X-rays (up to 10 keV and perhaps even more) with high sensitivity. We discuss the recent status of the development of very wide field X-ray telescopes as well as related scientific questions including expected major contributions such as monitoring and study of X-ray afterglows of Gamma Ray Bursts. ©2000 American Institute of Physics.