Analytical models of structure formation are an important tool, complementary to N-body simulations, to investigate the formation of cosmic structures and the dependence of their statistics on cosmological parameters. They rely on some non-linear map, typically spherical collapse, to relate topological features of the initial density field (number of maxima, minima, saddles, critical points...) to different types of structures and events (halos, voids, filaments, mergers...) in the cosmic web. I will give a broad introduction to the topic and discuss some recent developments. [please email a.held@imperial.ac.uk for zoom link or password]