[en] The strikingly anisotropic large-scale distribution of matter is made of an extended network of voids delimited by sheets, with filaments at their intersection which together form the cosmic web. Matter that will later form dark matter halos and their galaxies flows towards compact nodes at filaments' intersections and in the process, retains the imprint of the cosmic web. In this thesis, I predict the mass, accretion rate, and formation time of dark matter halos near proto-filaments (identified as saddle points of the potential) using a conditional version of the excursion set theory in its so-called up-crossing approximation. The (filament-type) saddle points provides a local frame in which to quantify the induced physical and morphological evolution of statistical properties of galaxies on large scales. The model predicts that at fixed mass, mass accretion rate and formation time vary with orientation and distance from the saddle, demonstrating that assembly bias is indeed susceptible to the tides imposed by the cosmic web. Starved, early-forming halos of smaller mass lie preferentially along the main axis of filaments, while more massive and younger halos are found closer to the nodes. Distinct gradients for distinct quantities such as typical mass and accretion rate occur because the saddle condition is anisotropic, and because the statistics of these observables depend on both the means and their covariances. The signature of this model corresponds at low redshift to an excess of reddened galaxies at fixed mass along preferred directions, as recently reported in spectroscopic (GAMA) and photometric (COSMOS) surveys and in hydrodynamic simulations (Horizon-AGN). I also compute the rate of merger events in the multi-scale initial conditions to forecast special events driving the anisotropic assembly of dark matter halos and understand their impact on galaxy formation. Beyond halo mergers, I consider all sets of mergers, including wall and filament mergers, as they impact the geometry of galactic infall. Their one- and two-points statistics are computed as a function of cosmic time. I establish the relation between merger rates and connectivity, which is then used to assess the impact the large scale structures on assembly bias. The anisotropy of the cosmic web, as encoded in this theory, is a significant ingredient to describe jointly the physics and dynamics of galaxies in their environment, e.g. in the context of intrinsic alignments or morphological diversity. In order to explore the impact of cosmic infall on smaller scales I implemented a novel tracer particles algorithm in the Eulerian adaptive mesh refinement code Ramses. The tracer particles are based on a Monte Carlo approach and keep tracks of where fluid elements originate, so as to follow their Lagrangian trajectories and re-processing history. I show that they reproduce the gas distribution very accurately and I extend them to also trace the stars and black holes through the full cycle of baryons. These tracer particles are ideal to study complex astrophysical systems where both the efficiency of shock-capturing Godunov schemes and a Lagrangian follow-up of the fluid are required simultaneously, in particular in cold flows. Thanks to this accurate tracer particle algorithm, the acquisition and loss of angular momentum of both cold and hot accretion flows onto galaxies at high redshift can be studied reliably. I find that the amplitude and orientation of the specific angular momentum of the cold gas is preserved down to the inner halo where the angular momentum contributes to the spin-up of galaxies, while for the hot gas it is lost at larger radii. Pressure torques, stronger in magnitude than gravitational torques are, however, spatially incoherent, which leads them to have no significant impact on the redistribution of angular momentum of the accretion flows. Gravitational torques, which dominate globally, are the main driver of the loss of angular momentum of the accretion flows in those halos, with dark matter gravitational torques dominating in the outer halo and stellar gravitational torques dominating in the disk. (author)