I will give an introduction to gas dynamics and star formation in the central region (R<3kpc) of the Milky Way. This region is dominated by the strongly non-axisymmetric gravitational potential of the Galactic bar. After reviewing the basic theoretical tools, I will discuss several topics including (i) how to interpret the observed longitude-velocity maps of CO, HI and other interstellar gas tracers; (ii) how we can use the gas dynamics to constrain the properties of the Galactic bar; (iii) how the gas is driven inwards from the Galactic disc (R~3kpc) down to the Central Molecular Zone (CMZ, R~120pc) and then to the circum-nuclear disc (R~3pc) that surrounds the central black hole SgrA*; (iv) the spatial and temporal distribution of star formation in the Galactic centre. Finally, I will highlight some open questions and directions of future research.