The Cosmic Web has been a familiar outcome of N-body simulations for about as long as there has been a World Wide Web, yet the most widely used analytic models of large-scale structure have still not incorporated it: Standard Perturbation Theory (SPT) stops at shell crossing; the Effective Field Theory (EFT) absorbs everything beyond into free counterterms that are marginalised over; Lagrangian Perturbation Theory (LPT) follows the flow up to the first sheets, but not through the multi-stream regime that follows; the halo model sticks to spherical collapse only.

In this talk I introduce the Web-Halo Model (WHM), which bridges LPT and the halo model with intermediate sheet and filament terms (one collapsed axis at a time), and show that it predicts the non-linear matter power spectrum to emulator precision with no fitted parameter up to the non-linear scale. The same ellipsoidal-collapse ingredients then enter a nested peak-background split (WHM-PBS), in which halo bias at fixed mass becomes a distribution: every halo inherits the bias of its host filament and sheet. In a short digression I use a completely different world map to explain the important concepts bias, stochasticity, assembly bias, and baryon feedback in a hopefully pedagogical way. The WHM-PBS then gives the first analytic explanation of why assembly bias moves haloes along the universal density-bias relations but off the tidal one, offers a mechanism for the inversion of the bias–concentration correlation at intermediate halo masses, and makes a physical, non-perturbative prediction of halo stochasticity.

I conclude with the potential of the WHM family to accurately predict the non-linear matter power spectrum for extended models, to describe the assembly bias of the primordial non-Gaussianity response, to supply physical priors on the nuisance parameters of EFT analyses, and to predict scale-dependent bias.