As waves approach the shore, their non-linear dynamics becomes increasingly important. Most of our understanding of wave non-linearity has resulted from theoretical work, laboratory experiments and field studies on beaches slopes steeper than about 1:40. There, very strong non-linear processes happen locally and on a short time scale, as demonstrated by narrow surf zones with plunging or collapsing breakers. The non-linearity on gently-sloping beaches, typical of high-energy dissipative environments, has a different character, as it can build up over a long period of time and along an extensive cross-shore area. This contribution serves to introduce the GLOBEX project, during which a high-resolution (in space and time) data set of the cross-shore evolution of short and infragravity waves was collected on a low-sloping (1:80) non-mobile laboratory beach. As non-linear transfers also occur in the vertical from the free-stream flow downwards into the bottom boundary layer, additional flow measurements performed with Laser Doppler Anemometry are also briefly presented.