According to the ΛCDM paradigm of cosmology, galaxies form at the centers of dark matter (DM) halos. While galaxy formation involves complex baryonic physics, the formation of DM halos is governed solely by gravity and cosmology. As a result, many of their properties exhibit a near scale-free behaviour, self-similar in either halo mass, cosmic time or both. This is especially true in the Einstein-de Sitter (EdS) regime, valid at redshifts z ≳ 1, when cosmological scaling relations become particularly simple, and in the narrow mass range of normal galaxies, where the fluctuation power spectrum can be approximated by a power law. Since many galaxy properties are strongly correlated with halo mass, they tend to exhibit a self-similar behaviour as well. A partial list of self-similar properties include the mass function of DM halos, the structure of the cosmic web, the accretion/merger rate of matter onto halos, the density profiles of DM halos and their angular momentum, which eventually determines the galaxy structure. We briefly review these below, and comment on how they can be used in conjunction with simple toy models to gain insight into galaxy formation.