This thesis describes two different analyses performed at LHCb using the B0s→φγ and B0→K∗0γ decay channels. First, the measurement of the ratio of branching fractions B(B0→K∗0γ)/B(B0s→φγ) is presented, giving the most precise value for B(B0s→φγ) to date. Secondly, the CP-violating observables S and C, as well as the mixing-induced A∆ parameter are measured through a time-dependent analysis of the B0s→φγ decay channel, this being the first time the S and C observables are probed in the Bs system. These studies are performed using data collected in 2011 and 2012 by the LHCb experiment at CERN, corresponding to an integrated luminosity of 3.0 fb−1 of pp collisions at a center-of-mass energy of 7 TeV and 8 TeV. The Standard Model (SM), which is the current theory of particle physics, has been widely tested, demonstrating an impressive predictive power. However, many questions remain open such as the observed bariogenesis in our universe or the apparent presence of dark matter. Therefore, different models of New Physics (NP) have been proposed to explain the remaining questions, which predict the existence of new particles or (and) new interactions. In parallel, the experimental community is focused on finding any hint of NP which might shed some light on the characteristics of the physics beyond the SM. Although no direct evidence for NP has been found at LHC so far, over the last few years indirect hints for NP have been reported by several experiments in the flavour sector (Belle, Babar, ATLAS, CMS and LHCb), increasing the interest on this particular field. In particular, deviations of the SM in observables related to lepton flavour universality violation are very intriguing.In this dissertation we focus on rare decays involving the b→sγ transition, which can only occur via loop diagrams. Hence, they are particularly sensitive to new heavy particles contributing in the loop, which allows to probe high energy scales through precision measurements. In these transitions, as a consequence of the chiral structure of the weak charged currents and the momentum conservation, the photon is predicted to be almost entirely left-handed polarized, which opens the possibility for a sensitive null test of the SM by measuring the right handed contributions.