A fundamental challenge in the theory of mean field games (MFGs) is that equilibria are generally non-unique in the absence of monotonicity assumptions. In this talk, we establish that an infinite-dimensional multiplicative common noise restores uniqueness for generic MFGs in one spatial dimension. Furthermore, by exploiting the connection between mean field control (MFC) and potential MFGs, we show that this common noise regularizes the MFC value function. Based on this regularity, we then construct optimal feedback controls for the MFC problem. This talk is based on joint work with F. Delarue.