  The total tau hadronic width can be accurately calculated using analyticity
and the operator product expansion. The result turns out to be very sensitive
to the value of alpha_s(m_tau^2), providing a precise determination of the
strong coupling constant. The theoretical description of this observable is
updated, including the recently computed O(alpha_s^4) contributions. The
experimental determination of alpha_s(m_tau^2) and its actual uncertainties are
discussed.
