Abstract: The field of Flavour Physics has been actively challenging the Standard Model in recent years, in particular in transitions involving a $b$ quark. These are the so-called $B$-anomalies, and discrepancies between experimental measurements and theoretical predictions have been found in different channels related to a $B$-meson decay: semileptonic currents, both charged and neutral, fully leptonic and also nonleptonic processes. Concerning the former, global analyses including all available experimental data on $b\to s\ell^+\ell^-$ observables reach global tensions of more than $7\sigma$. In other channels, individual observables already show discrepancies at the level of $2-3\sigma$. While this alone could make a compelling case for the need of New Physics to explain the current experimental data, what is most remarkable is the fact that one can establish coherent patterns linking all these apparently independent deviations.
In this Thesis we present an introduction to the different theoretical elements needed to describe the aforementioned $B$-anomalies within the framework of an Effective Field Theory, as well as the state-of-the-art results of our Global Fit to $b\to s\ell^+\ell^-$ observables. We also discuss individual tensions in observables of the charged semileptonic current $B\to D^*\ell\nu$ and also the nonleptonic $B_{d,s}\to K^{*0}\bar{K}^{*0}$ transition. On top of that, we also propose possible New Physics models that could bridge the gap between these different kinds of processes.