The late universe evolves from a nearly Gaussian primordial field into a complex network of filaments, sheets, halos, and voids. Analytic perturbation theory, numerical $N$-body simulations, and halo models are all used to describe this evolution.

The matter power spectrum $P(k)$ encodes the variance of density fluctuations in Fourier space, while the two-point correlation function $\xi(r)$ is its configuration-space counterpart. BAO appear as a preferred scale in both representations.

Collapsed halos can be modeled through spherical or ellipsoidal collapse thresholds and excursion-set theory. The halo mass function depends sensitively on the variance of the smoothed density field and the growth factor.

On small scales, nonlinear dynamics, feedback from star formation and active galactic nuclei, and baryonic physics can alter clustering. Precision cosmology therefore requires simulations and nuisance modeling to avoid biased inference.