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We survey some results on scalar curvature and properties of solutions to theEinstein constraint equations. Topics include an extended discussion ofasymptotically flat solutions to the constraint equations, including recentresults on the geometry of the center of mass of such solutions. We also reviewmethods to construct solutions to the constraint equations, including theconformal method, as well as gluing techniques for which it is important tounderstand both conformal and non-conformal deformations of the scalarcurvature.

Scalar Curvature and the Einstein Constraint Equations