VANDELS is a uniquely-deep spectroscopic survey of high-redshift galaxies with the VIMOS spectrograph on ESO's Very Large Telescope (VLT). The survey has obtained ultra-deep optical (0.48 < lambda < 1.0 micron) spectroscopy of ~2100 galaxies within the redshift interval 1.0 < z < 7.0, over a total area of ~0.2 sq. degrees centred on the CANDELS UDS and CDFS fields. Based on accurate photometric redshift pre-selection, 85% of the galaxies targeted by VANDELS were selected to be at z>=3. Exploiting the red sensitivity of the refurbished VIMOS spectrograph, the fundamental aim of the survey is to provide the high signal-to-noise ratio spectra necessary to measure key physical properties such as stellar population ages, masses, metallicities and outflow velocities from detailed absorption-line studies. Using integration times calculated to produce an approximately constant signal-to-noise ratio (20 < t_int < 80 hours), the VANDELS survey targeted: a) bright star-forming galaxies at 2.4 < z < 5.5, b) massive quiescent galaxies at 1.0 < z < 2.5, c) fainter star-forming galaxies at 3.0 < z < 7.0 and d) X-ray/Spitzer-selected active galactic nuclei and Herschel-detected galaxies. By targeting two extragalactic survey fields with superb multi-wavelength imaging data, VANDELS will produce a unique legacy data set for exploring the physics underpinning high-redshift galaxy evolution. In this paper we provide an overview of the VANDELS survey designed to support the science exploitation of the first ESO public data release, focusing on the scientific motivation, survey design and target selection.