In this talk I discuss several phenomena in cosmology wherein quantum behaviour appears to play an important role. This includes (i) axion dark matter, since there is macroscopic spreading of the wave-function, (ii) post-inflationary era, since modes begin at low occupancy, and (iii) scalar field tunneling, since it is usually thought to be forbidden classically. I then discuss how classical simulations can reproduce the quantum behavior by ensemble averaging, and mention applications and limitations.