To define a factor of i.i.d. process, we start with i.i.d. labels on the vertices of an infinite vertex-transitive graph. Then, each vertex gets a new label, which depends on the random labeling seen from there (given by an appropriate rule that is the same for all vertices). In the talk, we present a characterization of spectral measures of factor of i.i.d. processes. This provides a necessary condition for an invariant process to be factor of i.i.d. process, based on its covariance structure. Joint work with Balint Virag.