Crystal simulations: the road from the SPS to the LHC

The understanding of the crystal collimation and extraction experiments performed in the recent decade at CERN SPS, FNAL Tevatron, IHEP U-70 and RHIC is reviewed from the standpoint of Monte Carlo simulations. The expectations for the LHC - the crystal efficiency and the requirements to a crystal - are outlined basing on the same computer model verified in the above experiments. Finally, we discuss key issues for the future experiments at CERN SPS and Tevatron aiming to reach the most efficient channeling and to bring these tests to the future LHC as close as possible.