Symplectic geometry and contact geometry are closely related geometries in even and odd dimensions respectively. And there are two types of symplectic manifolds with contact boundary, the convex ones and the concave ones, depending on the direction of the Liouville vector field along the boundary. Convex symplectic manifolds, including the Stein domains, have been extensively studied in the past 30 years. The concave ones, which are more abundant and flexible, have received much less attention. I will discuss several aspects in dimension 4, including new perspectives for the concave ones.