The study of nuclear beta decay has guided our physical understanding of the universe throughout most of the 20th century, directly leading to the unification of electromagnetic and weak forces and the Standard Model. With new physics seemingly out of reach with modern colliders, low energy searches for Beyond Standard Model physics become even more valuable, consolidating the role of nuclear beta decay as physics moves forward. With experiments breaking new ground, we will review the theoretical progress on the beta spectrum shape and frame its role in ongoing and future tests of exotic currents in the weak interaction. We will analyze its position in the so-called reactor antineutrino anomaly which points towards the existence of a fourth, sterile neutrino. In doing so, we illustrate the influence of nuclear structure in the outstanding problems and conclusions.