Cosmology is a playground for several interesting aspects of theoretical physics. It is a discipline where large quantum effects can change the asymptotics of the spacetime and make it stochastic; where most-recent mathematical techniques can be used to study the fate of very inhomogenous universes, like ours before inflation, and to formulate no-global-singularity theorems; where particle-physics techniques can be applied to predict not only peculiar signals from inflation, but also the distribution of galaxies and extract unprecedented cosmological information from them. I will overview some of these aspects.