The recent imaging X-ray telescopes have quite limited field of view of order of 1 degree or so. The development of wide- field X-ray telescopes with large field of view, reasonable angular resolution and high sensitivity can play an important role in future of X-ray astronomy and astrophysics. An important alternative is the Lobster eye X- ray optics theoretically described in the past but not yet constructed and used in a real experiment. We review the wide-field X-ray optics arrangements and discuss their preferences and drawbacks. We report on the design, development, manufacture and tests of first test X-ray objectives based on both Angel and Schmidt lobster eye geometry. We also suggest strategy for further developments in this area and discuss the scientific importance of space experiments based on lobster eye optics.