The search and study of rare decays of B hadrons and of the $\tau$ lepton are among the most promising approaches of putting the Standard Model of particle physics to the test.
In recent years, the study of these decays, and in particular of flavour-changing neutral current decays $b\to s\ell\ell$, helped shed light on a set of tensions in the data with respect to theoretical predictions for branching ratios, angular distributions and lepton flavour universality.
In this work, the most recent results in the study of rare heavy-flavour decays at the Large Hadron Collider experiments are presented.