Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element \(V_{ud}\) and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, \emph{ab initio} nuclear many-body methods—grounded in realistic nucleon-nucleon interactions and systematically improvable approximations—have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art \emph{ab initio} calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., \(^{10}\)C \(\rightarrow\) \(^{10}\)B and \(^{14}\)O \(\rightarrow\) \(^{14}\)C) and allowed Gamow-Teller transitions (e.g., \(^{6}\)He\(\rightarrow\) \(^{6}\)Li, \(^{8}\)Li\(\rightarrow\) \(^{8}\)Be, \(^{8}\)B\(\rightarrow\) \(^{8}\)Be), where \emph{ab initio} calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of \emph{ab initio} calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.