LUX-ZEPLIN (L-Z) is a project to construct and operate a multi-tonne two-phase xenon detector for WIMP dark matter search. The detector will be built at the Sanford Underground Research Facility (South Dakota) at a depth of 4200 m.w.e. The Collaboration includes more than 30 institutions combining experienced teams from the LUX and ZEPLIN detectors, and from other searches for dark matter. The L-Z cryostat will contain 7 tonnes of liquid xenon inside the Time Projection Chamber target. 3 tonnes outside provides an anticoincidence system to reject background. Further rejection of neutron-induced background will use a liquid scintillator outer detector. The whole will be immersed in a water tank to protect against the radioactivity in the surrounding rock. I will present the status and describe the main elements of the detector. I will show how extensive material screening and associated Monte Carlo modelling reduce the experimental background.