  This Thesis presents my personal contributions to two distinct fields, namely
the recent experimental anomalies in B-meson decays, and the longstanding quest
for a theoretical explanation of lepton masses and mixings, under a unifying
umbrella: Flavour Physics. The modern view of the Standard Model as an
effective theory is motivated, and the dual role of flavour, as a probe of New
Physics effects on one side, and as a piece of the puzzle itself on the other,
is emphasized. By jointly discussing two physics cases of different nature, I
attempt to offer a broader perspective on the current status of Beyond Standard
Model searches. The discussion begins with a preliminary review of Standard
Model Effective Field Theories, in which some utility results in theory
matching are presented. The focus then moves to B-meson decay anomalies: after
introducing Lepton Flavour Universality, we discuss the phenomenology of a
specific Standard Model extension by scalar leptoquarks, and also present the
Effective Field Theory framework of Rank-One Flavor Violation, providing a less
detailed but broader picture for the case of neutral-current anomalies.
Finally, we tackle the Standard Model flavour puzzle, describing an attempt to
address charged lepton mass hierarchies in the framework of supersymmetric
modular invariant models of lepton flavour.
