We unfold a profound relationship between the dynamics of finite-size perturbations in spatially extended chaotic systems and the universality class of Kardar-Parisi-Zhang (KPZ). We show how this relationship can be exploited to obtain a complete theoretical description of the bred vectors dynamics. The existence of characteristic length/time scales, the spatial extent of spatial correlations and how to tune it, and the role of the breeding amplitude are all analyzed in the light of our theory. Implications to weather forecasting based on ensembles of initial conditions are also discussed.