  The search for New Physics (NP) beyond the Standard Model (SM) has been a
central focus of particle physics, including in the context of $B$-meson decays
involving $b \to s \ell \ell$ transitions. These transitions, mediated by
flavour-changing neutral currents, are highly sensitive to small NP effects due
to their suppression in the SM. While direct searches at colliders have not yet
led to NP discoveries, indirect probes through semi-leptonic decays have
revealed anomalies in observables such as the branching fraction $\mathcal{B}(B
\to K \mu \mu)$ and the angular observable $P_5'(B \to K^* \mu \mu)$. In order
to assess the observed tensions, it is essential to ensure an accurate SM
prediction. In this review, we examine the theoretical basis of the $B \to
K^{(*)} \ell \ell$ decays, addressing in particular key uncertainties arising
from local and non-local form factors. We also discuss the impact of QED
corrections to the Wilson coefficients, as well as the effect of CKM matrix
elements on the predictions and the tension with the experimental measurements.
We discuss the most recent results, highlighting ongoing efforts to refine
predictions and to constrain potential signs of NP in these critical decay
processes.
