I am interested in progress toward a deeper and more complete understanding of gravitation. We have an extensive understanding of the other three fundamental forces in the Standard Model (SM) in terms of local gauge theories formulated on a fixed Lorentz invariant background spacetime. General Relativity (GR) promotes gravitation to a special role among the fundamental forces in that it is relational or background-independent, i.e. the background spacetime is a dynamical degree of freedom in GR.
One interesting line of investigation is to try and formulate GR itself as a local gauge theory in parallel to the other fundamental forces and see exactly how the relational nature of GR emerges in this setting. The importance of this is that we have a good understanding of how to consistently quantize the gauge theories of the SM, while at present our understanding of how to quantize gravity is incomplete. The leading candidate for a consistent quantum theory of gravity, String Theory, is presently best understood in a perturbative and background dependent formulation.
Despite these shortcomings, the incredible wealth of ideas and tools emerging from such a tightly constrained theory motivates continued exploration of the subject and in particular any progress on nonperturbative and/or background independent formulations.