<p>Trilayer Ruddlesden-Popper phase La₄Ni₃O₁₀ has been observed with <i>T</i>_<i>c</i> of ∼30 K at high pressure in a recent experiment, which further expanded the family of nickelate superconductors. In this study, we explored the effects of electronic correlations in La₄Ni₃O₁₀ using density functional theory plus dynamical mean-field theory at ambient and high pressures. Our derived spectral functions and Fermi surface of the ambient pressure phase are nicely consistent with the experimental results by angle-resolved photoemission spectroscopy, which emphasized the importance of electronic correlations in La₄Ni₃O₁₀. We also found the electronic correlations in pressurized La₄Ni₃O₁₀ are both orbital-dependent and layer-dependent due to the presence of Hund’s rule coupling. There is a competition between the Hund’s rule coupling and the crystal-field splitting, and therefore, the Ni–O layers with weaker crystal-field splitting energy would have stronger electronic correlations.</p>