Much of our understanding of heavy fermion systems over the past two decades has been based on the single impurity model and its approximate solutions. We show with numerous examples of photoelectron spectra, especially with YbInCu4, that this model is not applicable to stoichiometric heavy fermion compounds. There is overwhelming evidence that the correct description of heavy fermions must include very narrow, hybridized bands which exist already at temperatures far above the thermodynamically determined Kondo temperature, and that these bands are relatively temperature independent. Some form of the periodic Anderson model (PAM) is needed, one which results in very narrow renormalized LDA bands. We compare our data to one form of the PAM. © 2001 Elsevier Science B.V.