  The beam aperture of a particle accelerator defines the clearance available
for the circulating beams and is a parameter of paramount importance for the
accelerator performance. At the CERN Large Hadron Collider (LHC), the knowledge
and control of the available aperture is crucial because the nominal proton
beams carry an energy of 362 MJ stored in a superconducting environment. Even a
tiny fraction of beam losses could quench the superconducting magnets or cause
severe material damage. Furthermore, in a circular collider, the performance in
terms of peak luminosity depends to a large extent on the aperture of the inner
triplet quadrupoles, which are used to focus the beams at the interaction
points. In the LHC, this aperture represents the smallest aperture at
top-energy with squeezed beams and determines the maximum potential reach of
the peak luminosity. Beam-based aperture measurements in these conditions are
difficult and challenging. In this paper, we present different methods that
have been developed over the years for precise beam-based aperture measurements
in the LHC, highlighting applications and results that contributed to boost the
operational LHC performance in Run 1 (2010-2013) and Run 2 (2015-2018).
