Despite small branching fractions, the $H \to \gamma\gamma$ and $H \to ZZ^* \to 4\ell$ Higgs boson decays provide clean and well reconstructed final states, allowing for precise measurements of the Higgs boson properties. These proceedings present measurements of total and differential fiducial cross sections in the $H \to \gamma\gamma$ and $H \to ZZ^* \to 4\ell$ decay channels, and a mass measurement in the $H \to ZZ^* \to 4\ell$ decay channel. The total fiducial cross section is measured to be $\sigma^{\gamma\gamma}_{\text{fid}} = 65.2 \pm 7.1$ fb in the $H \to \gamma\gamma$ channel and $\sigma^{4\ell}_{\text{fid}} = 3.28 \pm 0.32$ fb in the $H \to ZZ^* \to 4\ell$ channel, in agreement with the Standard Model predictions. Differential cross-section measurements are reported for Higgs boson production- and decay-related observables. The Higgs boson transverse momentum differential cross-section distributions are used to constrain the charm Yukawa coupling modifier (95% confidence level interval on $\kappa_c$ of $[-12, 11]$ in the $H \to 4\ell$ analysis and of $[-19, 24]$ in the $H \to \gamma\gamma$ analysis). Other differential distributions allow constraints on pseudo-observables and effective field theory coefficients. The Higgs boson mass in the $H \to ZZ^* \to 4\ell$ decay channel is measured to be $m_H = 124.92 \pm 0.19 \, \text{(stat.)}^{+0.09}_{-0.06} \, \text{(sys.) }$ GeV. All the results are derived using 139 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collisions collected with the ATLAS detector during the Run 2 of the LHC.