  Following the discovery of the Kondo effect the bulk transport and magnetic
behavior of the dilute magnetic alloys have been successfully described. In the
last fifteen years new directions have been developed as the study of the
systems of reduced dimensions and the artificial atoms so called quantum dots.
In this review the first subject is reviewed starting with the scanning
tunneling microscope (STM) study of a single magnetic impurity. The next
subject is the reduction of the amplitude of the Kondo effect in samples of
reduced dimension which was explained by the surface magnetic anisotropy which
blocks the motion of the integer spin nearby the surface. The electron
dephasing and energy relaxation experiments are discussed with the possible
explanation including the surface anisotropy, where the situation in cases of
integer and half-integer spins is very different. Finally, the present
situation of the theory of dynamical structural defects is briefly presented
which may lead to two-channel Kondo behavior.
