Abstract WEAVE, the new wide-field, massively multiplexed spectroscopic survey facility for the William Herschel Telescope, will see first light in late 2022. WEAVE comprises a new 2-degree field-of-view prime-focus corrector system, a nearly 1000-multiplex fibre positioner, 20 individually deployable ‘mini’ integral field units (IFUs), and a single large IFU. These fibre systems feed a dual-beam spectrograph covering the wavelength range 366−959 nm at R ∼ 5000, or two shorter ranges at R ∼ 20 000. After summarising the design and implementation of WEAVE and its data systems, we present the organisation, science drivers and design of a five- to seven-year programme of eight individual surveys to: (i) study our Galaxy’s origins by completing Gaia’s phase-space information, providing metallicities to its limiting magnitude for ∼3 million stars and detailed abundances for ∼1.5 million brighter field and open-cluster stars; (ii) survey ∼0.4 million Galactic-plane OBA stars, young stellar objects and nearby gas to understand the evolution of young stars and their environments; (iii) perform an extensive spectral survey of white dwarfs; (iv) survey ∼400 neutral-hydrogen-selected galaxies with the IFUs; (v) study properties and kinematics of stellar populations and ionised gas in z < 0.5 cluster galaxies; (vi) survey stellar populations and kinematics in ∼25 000 field galaxies at 0.3 ≲ z ≲ 0.7; (vii) study the cosmic evolution of accretion and star formation using >1 million spectra of LOFAR-selected radio sources; (viii) trace structures using intergalactic/circumgalactic gas at z > 2. Finally, we describe the WEAVE Operational Rehearsals using the WEAVE Simulator.