We use hydrodynamical simulations to study the Milky Ways 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 $Rsim 5kpc$. Our main findings are as follows: (1) The distinction between inner ($Rlesssim120$~pc) and outer ($120lesssim Rlesssim450$~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 $Rsimeq 200$~pc which includes the 1.3$^circ$ 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 $infty$-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 ($Rsimeq 3$~kpc) down to the CMZ ($Rsimeq200$~pc) of the order of $1rm,M_odot,yr^{-1}$, consistent with observational determinations. (4) Supernova feedback can drive an inflow from the CMZ inwards towards the circumnuclear disc of the order of $sim0.03,rm M_odot,yr^{-1}$. (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 ($Rlesssim30$~pc) to the Galactic centre, but are also connected to the larger-scale streams at $Rgtrsim100$~pc.
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