I will present recent mathematical developments on self-gravitating massive fields. First, in collaboration with Yue Ma, I established the global nonlinear stability of self-gravitating Klein-Gordon fields in the regime near Minkowski spacetime, when the metric enjoys only low decay conditions at spacelike infinity. The proposed strategy of proof, referred to as the Euclidean-Hyperboloidal Foliation Method, applies more generally to nonlinear wave-Klein-Gordon systems. Second, the Seed-to-Solution Method introduced in collaboration with T.-C. Nguyen generates classes of asymptotically Euclidean manifolds satisfying Einstein's constraint equations under prescribed asymptotic conditions at infinity. Motivated by Carlotto and Schoen’s optimal localization problem, we formulated and solved an asymptotic localization problem. Furthermore, Einstein's constraint equations also play a central role in understanding spacetimes in the vicinity of singularity hypersurfaces, and a recent work in collaboration with B. Le Floch and G. Veneziano provides a large class of bouncing cosmological spacetimes.