Abstract  We have entered the era of high precision cosmology. The seeds that formed the gravitationally bound structures in the Universe can be extrapolated from the cosmic microwave background fluctuations. The matter-energy content of the Universe is well defined within the concordant LCDM paradigm and we can now unambiguously associate a cosmic epoch to any redshift to follow galaxy formation and evolution through cosmic time. This paradigm sets a rather rigid framework for structure formation that can be compared to the observed growth rate of structures in the Universe. In parallel, our understanding of galaxy formation has evolved from a classical picture – in which galaxies grow through stochastic starbursts driven by the hierarchical growth of structures and its associated numerous mergers of galaxies – to a rather different picture that recalls the old monolithic collapse of galaxies. In this new picture, dark matter gravitational potential wells seem to control the growth rate of galaxies through their attractive power on the diffuse intergalactic medium. A growth that is modulated by supernova explosions and active galactic nuclei, supposed to act against gravity.We will show that when we try to bridge the cosmological and structure formation frameworks a tension emerges. Behind this tension stands the question of whether we are only seeing the result of the incomplete treatment of baryonic physics, the so-called “gastrophysics”, or whether we are missing some fundamental physics either at the galaxy scale (role of the magnetic field, cosmic rays,…) or at a more fundamental scale (nature of dark matter,…).