The major improvement in the step from LDA to GGA comes from improved modelling of the exchange approximation. Becke's parameterization was fitted to reproduce the exchange energies of the rare-gas atoms, and Perdew's nonempirical GGA approximation of the exchange hole likewise considerably improved atomic exchange energies. The main contribution to the success of GGA (improvement over LDA) for bonds in simple diatomic molecules originates from these exchange improvements. This is mystifying since one would expect the better exchange approximation of GGA to reproduce more closely the poor Hartree-Fock results. Apparently, the GGA exchange improvements have turned the exchange holes into better exchange-correlation holes. So, there is still a considerable lack of precise understanding why the most successful models work, which perhaps explains the lack of consistent improvement beyond the GGA level. On the other hand, the "physical route" to the correlation problem by modelling of the exchange-correlation hole is hopefully a fruitful way forward that can be pursued independently of the clarification of the mathematical intricacies of DFT.