Poincare-Einstein metrics are a natural class of complete Einstein metrics with negative Einstein constant, though their construction is often difficult. In this talk, I will discuss four-dimensional conformally Kahler Poincare-Einstein metrics. In this setting, the conformally Kahler structure reduces the Einstein equation to a single nonlinear elliptic equation of Toda type, yielding an infinite-dimensional, nonperturbative construction of Poincare-Einstein metrics. I will then explain how the same framework extends to metrics with various cusp ends and how it can be used to study degenerations of Poincare-Einstein metrics. This provides a unified analytic perspective on several noncompact Einstein geometries through elliptic boundary value problems. This is joint work with Mingyang Li.