We use hydrodynamical simulations to study the Milky Way’s central molecular zone (CMZ). The simulations include a non-equilibrium chemical network, the gas self-gravity, star formation and supernova feedback. We resolve the structure of the interstellar medium at sub-parsec resolution while also capturing the interaction between the CMZ and the bar-driven large-scale flow out to R ∼ 5 kpc. Our main findings are as follows: (1) The distinction between inner (R ≲ 120 pc) and outer (120 ≲ R ≲ 450 pc) CMZ that is sometimes proposed in the literature is unnecessary. Instead, the CMZ is best described as single structure, namely a star-forming ring with outer radius R ≃ 200 pc which includes the 1.3○ complex and which is directly interacting with the dust lanes that mediate the bar-driven inflow. (2) This accretion can induce a significant tilt of the CMZ out of the plane. A tilted CMZ might provide an alternative explanation to the ∞-shaped structure identified in Herschel data by Molinari et al. 2011. (3) The bar in our simulation efficiently drives an inflow from the Galactic disc (R ≃ 3 kpc) down to the CMZ (R ≃ 200 pc) of the order of $1\rm \, M_\odot \, yr^{-1}$, consistent with observational determinations. (4) Supernova feedback can drive an inflow from the CMZ inwards towards the circumnuclear disc of the order of $\sim 0.03\, \rm M_\odot \, yr^{-1}$. (5) We give a new interpretation for the 3D placement of the 20 and 50 km s−1 clouds, according to which they are close (R ≲ 30 pc) to the Galactic centre, but are also connected to the larger-scale streams at R ≳ 100 pc.