According to the symmetrization postulate, a wave function of N identical particles must be either symmetric (bosons) or anti-symmetric (fermions). It may be surprising that not all wave functions have to be symmetric, and it may also be surprising that arbitrary asymmetric wave functions cannot occur. I will review the extent to which this fact can be explained. The relevant explanations are connected to the non-trivial topology of the configuration space of N identical particles, i.e., the space of unordered configurations. This is joint work with Shelly Goldstein, James Taylor, and Nino Zanghi (and influenced by Detlef).