In this paper we review the present status of electron spectroscopy of
Ce and Yb Kondo systems, with particular emphasis on photoemission an
d inverse photoemission. Our starting point is the situation in the mi
d-1980s, characterized by the development of a 'Kondo scenario' for th
e thermodynamic and spectral properties, as described in the review by
Allen et al. (1986, Adv. Phys., 35, 275). That picture, based on room
-temperature results and on a T=0 approach to the impurity Anderson Ha
miltonian, has been generally confirmed and better defined over the pa
st decade by a number of more elaborate experiments, and by new calcul
ational schemes. The use of high-energy resolution and cryogenic tempe
ratures has led to the direct observation of the characteristic low-en
ergy excitations and has opened the way to stringent tests of the most
fundamental aspect of model, namely its scaling properties. Despite t
he success of the Kondo approach, more work remains to be done. The im
proved quality of the data has revealed some quantitative discrepancie
s with the predictions of the model, stressing the need for more reali
stic theoretical schemes. Moreover, some recent experiments questionin
g the validity of the model have stirred a fierce controversy within t
he spectroscopic community. We review those conflicting results and di
scuss the possible reasons for the discrepancies, and how new experime
nts could solve the present difficulties.