1. Introduction
2. New mock catalogs for X-ray simulations
2.1. The SIXTE software
2.2. AGN mock catalog
2.3. Galaxy mock catalog
2.4. Galaxy clusters mock catalog
2.5. Consistency with the cosmic X-ray background
3. The AXIS probe
3.1. The complementary strengths of AXIS and Athena
4. Results of the simulations of AGN surveys with AXIS
4.1. Simulations and source detection
4.2. AXIS Deep Field results
4.3. AXIS Intermediate Field results
4.4. AXIS Wide Field results
5. The high-redshift Universe as seen by Athena and AXIS
5.1. Extragalactic surveys with Athena –WFI
5.2. A new X-ray view of the high-redshift Universe
5.3. Heavily obscured black hole accretion in the early Universe
6. Summary and conclusions