tokens: different resolution elements (gas, DM, stars and BHs); the solution of the (magneto)hydrodynamical equations for the gaseous component; a treatment of the most important radiative cooling and heating processes; a mechanism for the conversion of gas into stars; stellar evolution and subsequent chemical enrichment of the interstellar, circumgalactic and intergalactic medium; outflows of gas from the star-forming regions of galaxies; and the formation, growth and energetic feedback of supermassive BHs in distinct low- and high-accretion rate states. In developing the TNG model, we have pursued three simultaneous goals: to bring together under a consistent framework the improvements implemented in arepo to the accuracy and robustness of the underlying numerical methods; to introduce new, rich physics; and to address the key deficiencies of the previous model. The main numerical updates are summarized in Section 2.2 and include an improved estimator for spatial gradients across gas cells, a more efficient gravity solver and time integration scheme, and a more consistent advection of the passive scalars. Together, these changes give a more accurate and better convergent hydrodynamical scheme, and will allow us to pursue even more ambitious simulations in the future. The principal new physics in the TNG model are the inclusion of MHD (see Section 2.2.1 and references therein) and a dual-mode, thermal and kinetic BH feedback model (see the companion paper by Weinberger et al. 2017 ). The new kinetic BH feedback has been shown to alleviate some of the discrepancies identified in Illustris in comparison to observations at the high end of the halo mass function ( ≳ 10 12 –10 14 M ⊙ ), in particular regulating the stellar content of massive galaxies while preserving realistic halo gas fractions. In fact, in confronting the problems identified in Illustris (see Introduction section), we aim to open new physical regimes that were impossible to robustly study in previous simulations. These include not only massive haloes emitting at X-ray wavelengths, but also the galaxies occupying the transitional green valley, and the properties of low-mass dwarfs, including cluster satellite populations. In this paper, we have focused on the intermediate- and low-mass end of the galaxy population (halo masses of a few 10 10 –10 13 M ⊙ ) and have presented an updated model for the galactic winds feedback by modifying their directionality, thermal content, velocity and energy scalings (Section 2.3.2 ). We have also updated our reference yield tables (Table 2 and Fig. 1 ) and adjusted some stellar evolution choices (Section 2.3.3 ). The TNG galactic winds (whose implementation and scalings largely follow those of Springel Hernquist 2003 ; Oppenheimer Davé 2006 ; Oppenheimer Davé 2008 ; Vogelsberger et al. 2013 ) are now launched isotropically from the star-forming regions of galaxies, bringing a simplification to the modelling that by itself does not significantly affect
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