Here are two possibly relevant references, a decade apart (1998 and 2008), neither of which I can knowledgeably assess:

(1) Thierry Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer Monographs in Mathematics, 1998.

(2) Simon Donaldson, "Some problems in differential geometry and topology," Nonlinearity 21 T157, 2008.

Here is one sentence from Donaldson's paper:

The outstanding problem then, in 4-manifold topology, is to find if there is something which could play the role of Thurston’s geometrization conjecture, for the case of 3-manifolds, and which might guide further research.