  At the Tevatron, the total p_bar-p cross-section has been measured by CDF at
546 GeV and 1.8 TeV, and by E710/E811 at 1.8 TeV. The two results at 1.8 TeV
disagree by 2.6 standard deviations, introducing big uncertainties into
extrapolations to higher energies. At the LHC, the TOTEM collaboration is
preparing to resolve the ambiguity by measuring the total p-p cross-section
with a precision of about 1 %. Like at the Tevatron experiments, the
luminosity-independent method based on the Optical Theorem will be used. The
Tevatron experiments have also performed a vast range of studies about soft and
hard diffractive events, partly with antiproton tagging by Roman Pots, partly
with rapidity gap tagging. At the LHC, the combined CMS/TOTEM experiments will
carry out their diffractive programme with an unprecedented rapidity coverage
and Roman Pot spectrometers on both sides of the interaction point. The physics
menu comprises detailed studies of soft diffractive differential
cross-sections, diffractive structure functions, rapidity gap survival and
exclusive central production by Double Pomeron Exchange.
