In this project we aim to deepen our understanding of semileptonic processes within the Standard Model (SM) and its extensions (BSM). Semileptonic decays of hadrons containing a b-quark serve as an ideal testing ground, as they are intricately linked to the heaviest known particle - the top quark - which is anticipated to be most affected by BSM physics. Furthermore, such decays enable the testing of lepton flavour universality (LFU), a fundamental prediction of the Standard Model. Recent experimental and theoretical activities in LFU have been prompted by hints of discrepancies between SM predictions and observations in LFU ratios such as R(D) and R(D*).In our study of the semileptonic decay B -> D l nu, we aim to establish robust links between theoretical (B)SM predictions and experimental observations. Specifically, our goal is to provide a refined evaluation of electromagnetic effects in the LFU-probing observable ratio R(D).Additionally, we will explore the effects of CP-violating couplings in semileptonic processes at the Large Hadron Collider (LHC). In this part we will propose CP-odd differential observables in semileptonic process pp -> b c tau nu and related processes. These observables are designed to be sensitive to exclusively to CP-violating scenarios of BSM that address the R(D) and R(D*) anomalies.Furthermore, our research extends to inclusive decays of heavy hadrons, focusing on b-baryons within the heavy quark expansion (HQE) framework. We aim to scrutinise forward matrix elements of effective operators by leveraging recent lattice QCD determinations and small velocity sum rules, thereby enhancing our understanding of non-perturbative effects and corresponding implications for experimental measurements.The anticipated outcomes of this project will improve our theoretical insights and guide flavour physics experiments at low energies as well as at high-pT experiments at the LHC.