  Recently published and preliminary results of the TOTEM experiment are
presented, emphasizing a recent discovery of a non-exponential behaviour of the
differential cross-section of elastic proton-proton scattering, that TOTEM
measured with an unprecedented precision at the centre-of-mass energy
$\sqrt{s}$ = 8 TeV based on a high-statistics data sample obtained with the
$\beta_* = 90$ m optics of CERN LHC. Both the statistical and systematic
uncertainties remained below 1%, except for the t-independent contribution from
the overall normalisation. This measurement allowed TOTEM to exclude a purely
exponential differential cross-section in the range of four-momentum transfer
squared 0.027 < |t| < 0.2 GeV$^2$ with a significance greater than 7 $\sigma$.
In this context we also highlight the innovative TOTEM recalibration of LHC
optics, that used elastic scattering data measured by the world's largest and
most complex Roman Pot detector system, and discuss recent preliminary TOTEM
data on the Coulomb-Nuclear interference region with its physics implications.
