The Taipan galaxy survey (hereafter simply ‘Taipan’) is a multi-object spectroscopic survey starting in 2017 that will cover 2π steradians over the southern sky (δ ≲ 10°, |b| ≳ 10°), and obtain optical spectra for about two million galaxies out to z < 0.4. Taipan will use the newly refurbished 1.2-m UK Schmidt Telescope at Siding Spring Observatory with the new TAIPAN instrument, which includes an innovative ‘Starbugs’ positioning system capable of rapidly and simultaneously deploying up to 150 spectroscopic fibres (and up to 300 with a proposed upgrade) over the 6° diameter focal plane, and a purpose-built spectrograph operating in the range from 370 to 870 nm with resolving power R ≳ 2000. The main scientific goals of Taipan are (i) to measure the distance scale of the Universe (primarily governed by the local expansion rate, H0) to 1% precision, and the growth rate of structure to 5%; (ii) to make the most extensive map yet constructed of the total mass distribution and motions in the local Universe, using peculiar velocities based on improved Fundamental Plane distances, which will enable sensitive tests of gravitational physics; and (iii) to deliver a legacy sample of low-redshift galaxies as a unique laboratory for studying galaxy evolution as a function of dark matter halo and stellar mass and environment. The final survey, which will be completed within 5 yrs, will consist of a complete magnitude-limited sample (i ⩽ 17) of about 1.2 × 106 galaxies supplemented by an extension to higher redshifts and fainter magnitudes (i ⩽ 18.1) of a luminous red galaxy sample of about 0.8 × 106 galaxies. Observations and data processing will be carried out remotely and in a fully automated way, using a purpose-built automated ‘virtual observer’ software and an automated data reduction pipeline. The Taipan survey is deliberately designed to maximise its legacy value by complementing and enhancing current and planned surveys of the southern sky at wavelengths from the optical to the radio; it will become the primary redshift and optical spectroscopic reference catalogue for the local extragalactic Universe in the southern sky for the coming decade.