I will discuss solutions of Einstein equations on non-compact complete manifolds that are conformal to metrics on compact manifolds with boundary. For such metrics, there is a notion of 'boundary at infinity' that is determined up to a conformal factor. We consider the problem of finding an Einstein metric that has the prescribed conformal boundary. In this talk I will give the definitions and early results in the theory and also describe some of our results for 5-manifolds with symmetry.