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Measurements of angular correlations between initial and final particles in$\beta$ decay remain one of the most promising ways of probing the StandardModel and looking for new physics. As experiments reach unprecedented precisionwell into the per-mille regime, proper extraction of results requires one totake into account a great number of nuclear structure and radiative correctionsin a procedure which becomes dependent upon the experimental geometry. Weprovide here a compilation and update of theoretical results which describe allcorrections in the same conceptual framework, point out pitfalls and review theinfluence of the experimental geometry. Finally, we summarize the potential fornew physics reach.

Consistent description of angular correlations in $\beta$ decay for Beyond Standard Model physics searches