Post-Newtonian Approximations, Compact Binaries, and Strong-Field Tests of Gravity

This is an extended summary of the two parallel sessions held at MG11: PPN1 Strong Gravity and Binaries'' (chaired by L.B. and L.G.) and PPN2 Post-Newtonian Dynamics in Binary Objects’’ (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places the delivered talks in a broader perspective of current studies in this area. One can find more details in individual contributions of the respective authors.