Stein manifolds are special compact subsets of affine algebraic varieties which play an important role in complex/symplectic geometry and singularity theory. Due to Eliashberg's topological characterization, the existence and uniqueness of Stein structures on n-dimensional manifolds are well-understood for n>4, but are more challenging when n=4. I will give a brief survey on these problems and talk about a recent construction done in collaboration with Oba and Ukida.