The goal of this conference is to gather theorists, simulators and observers to brainstorm over the structure of the cosmic web and its influence on galaxy properties. In particular we wish to address the following points: -our theoretical understanding of the cosmic web, its dynamics and evolution (3D structure of the dark matter field, impact of the nature of dark matter on structure formation, mechanism of acquisition of angular momentum of collapsed structures, the dynamics and persistence of cold streams); - the characterization of the components of the cosmic web, i.e. nodes, filaments, walls and voids: what are the different techniques to extract them from simulations and observations? - Numerical predictions and observational signatures of the influence of the cosmic web on galaxy properties (cold streams, cosmic gas accretion as regulator of star-formation and galaxy growth, CGM physics, feedback, metal enrichment); - Challenges: 3D spectroscopy, HI surveys, reconstruction of density fields from galaxy surveys, zoom-in techniques in simulation. Questions and comments should be sent to: aix2015 lam.fr Web site available here : http://aix2015.lam.fr/