The EAGLE project, led by the Virgo Consortium, is a suite of hydrodynamical simulations that model the formation and evolution of galaxies and supermassive black holes in a cosmologically realistic ΛCDM universe. The simulations aim to improve the understanding of galaxy formation by addressing limitations such as finite resolution and poorly constrained subgrid physics. A key improvement is the treatment of feedback from massive stars and active galactic nuclei (AGN), where thermal energy is injected into the gas without turning off cooling or hydrodynamic forces, allowing winds to develop naturally. The feedback efficiencies are calibrated to match the observed galaxy stellar mass function and the relation between galaxy-central black hole masses, with the observed galaxy stellar mass function reproduced to within ≲ 0.2 dex over the mass range 10^8 < M_s/M_0 ≲ 10^11. The simulations show good agreement with observed observables such as specific star formation rates, passive fractions, the Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic C IV and O VI. While the mass-metallicity relations for gas and stars are consistent with observations for M_s ≳ 10^9 M_0 (M_s ≳ 10^10 M_0 at intermediate resolution), they are insufficiently steep at lower masses. The EAGLE simulation suite includes higher-resolution zoomed-in volumes and variations in numerical techniques and subgrid models, providing a valuable resource for studying galaxy formation. The project discusses the implications of subgrid models for feedback on the predictive power of simulations and the role of numerical convergence, emphasizing the need for calibration to reproduce observed observables.The EAGLE project, led by the Virgo Consortium, is a suite of hydrodynamical simulations that model the formation and evolution of galaxies and supermassive black holes in a cosmologically realistic ΛCDM universe. The simulations aim to improve the understanding of galaxy formation by addressing limitations such as finite resolution and poorly constrained subgrid physics. A key improvement is the treatment of feedback from massive stars and active galactic nuclei (AGN), where thermal energy is injected into the gas without turning off cooling or hydrodynamic forces, allowing winds to develop naturally. The feedback efficiencies are calibrated to match the observed galaxy stellar mass function and the relation between galaxy-central black hole masses, with the observed galaxy stellar mass function reproduced to within ≲ 0.2 dex over the mass range 10^8 < M_s/M_0 ≲ 10^11. The simulations show good agreement with observed observables such as specific star formation rates, passive fractions, the Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic C IV and O VI. While the mass-metallicity relations for gas and stars are consistent with observations for M_s ≳ 10^9 M_0 (M_s ≳ 10^10 M_0 at intermediate resolution), they are insufficiently steep at lower masses. The EAGLE simulation suite includes higher-resolution zoomed-in volumes and variations in numerical techniques and subgrid models, providing a valuable resource for studying galaxy formation. The project discusses the implications of subgrid models for feedback on the predictive power of simulations and the role of numerical convergence, emphasizing the need for calibration to reproduce observed observables.