Phenomenology of the Higgs and flavour physics in the Standard Model and beyond

This thesis investigates some future aspects of Higgs measurements a decade after its discovery, focusing on the potential for future runs of the Large Hadron Collider (LHC). In particular, it aims to probe challenging couplings of the Higgs like its self-coupling and interaction with light quarks. The first part provides an overview of Higgs physics within the Standard Model Effective Field theory (SMEFT). The second part is about single-Higgs production, starting with a two-loop calculation of the gluon fusion component of Zh to reduce its theoretical uncertainties. Then, the potential for constraining the Higgs trilinear self-coupling from single Higgs rates is revisited; by including equally weakly-constrained four-heavy-quark operators entering at the next-to-leading order in single Higgs rates. These operators highly correlate with the trilinear self-coupling, thus affecting the fits made on this coupling from single Higgs data. The third part focuses on the Higgs pair production, an essential process for measuring Higgs-self coupling, employing multivariate analysis to study its potential for probing light Yukawa couplings; thereby exploring the sensitivity of Higgs pair production for the light-quark Yukawa interactions. Finally, the fourth part showcases some models aiming to explain the recent flavour anomalies in the light of a global SMEFT Bayesian analysis combining flavour and electroweak precision measurements.