  Measurements of angular correlations between initial and final particles in
$\beta$ decay remain one of the most promising ways of probing the Standard
Model and looking for new physics. As experiments reach unprecedented precision
well into the per-mille regime, proper extraction of results requires one to
take into account a great number of nuclear structure and radiative corrections
in a procedure which becomes dependent upon the experimental geometry. We
provide here a compilation and update of theoretical results which describe all
corrections in the same conceptual framework, point out pitfalls and review the
influence of the experimental geometry. Finally, we summarize the potential for
new physics reach.
