  We review the context, the motivations and the expected performances of a
comprehensive and ambitious fixed-target program using the multi-TeV proton and
ion LHC beams. We also provide a detailed account of the different possible
technical implementations ranging from an internal wire target to a full
dedicated beam line extracted with a bent crystal. The possibilities offered by
the use of the ALICE and LHCb detectors in the fixed-target mode are also
reviewed.
