After introducing the Incompressible Porous Media (IPM) equation and its stratified steady states, I will present a recent result - obtained in collaboration with Jo, Park, and Wang - on the sharp asymptotic stability of IPM near stable stratified density profiles. This result is sharp in that it resolves the gap between small-data global well-posedness and strong ill-posedness for IPM in the vicinity of stable stratified states, and it exploits the variational structure underlying the dynamics.