  Lattice QCD has reached a mature status. State of the art lattice
computations include $u,d,s$ (and even the $c$) sea quark effects, together
with an estimate of electromagnetic and isospin breaking corrections for
hadronic observables. This precise and first principles description of the
standard model at low energies allows the determination of multiple quantities
that are essential inputs for phenomenology and not accessible to perturbation
theory.
  One of the fundamental parameters that are determined from simulations of
lattice QCD is the strong coupling constant, which plays a central role in the
quest for precision at the LHC. Lattice calculations currently provide its best
determinations, and will play a central role in future phenomenological
studies. For this reason we believe that it is timely to provide a pedagogical
introduction to the lattice determinations of the strong coupling. Rather than
analysing individual studies, the emphasis will be on the methodologies and the
systematic errors that arise in these determinations. We hope that these notes
will help lattice practitioners, and QCD phenomenologists at large, by
providing a self-contained introduction to the methodology and the possible
sources of systematic error.
  The limiting factors in the determination of the strong coupling turn out to
be different from the ones that limit other lattice precision observables. We
hope to collect enough information here to allow the reader to appreciate the
challenges that arise in order to improve further our knowledge of a quantity
that is crucial for LHC phenomenology.
