  The study of lepton flavor universality violation (LFUV) in semitauonic
$b$-hadron decays has become increasingly important in light of longstanding
anomalies in their measured branching fractions, and the very large datasets
anticipated from the LHC and Belle II. In this review, we undertake a
comprehensive survey of the experimental environments and methodologies for
semitauonic LFUV measurements at the $B$-factories and LHCb, along with a
concise overview of the theoretical foundations and predictions for a wide
range of semileptonic decay observables. We proceed to examine the future
prospects to control systematic uncertainties down to the percent level,
matching the precision of Standard Model (SM) predictions. Furthermore, we
discuss new perspectives and caveats on combinations of the LFUV data and
revisit the world averages for the ${\cal R}(D^{(*)})$ ratios. Here we
demonstrate that different treatments for the correlations of uncertainties
from $D^{**}$ excited states can vary the current $3\sigma$ tension with the SM
within a $1\sigma$ range. Prior experimental overestimates of $D^{**}\tau\nu$
contributions may further exacerbate this. The precision of future measurements
is also estimated; their power to exploit full differential information, and
solutions to the inherent difficulties in self-consistent new physics
interpretations of LFUV observables, are briefly explored.
