A Stein manifold can be defined as complex manifold which admits a proper holomorphic embedding into C^n and their study lies at the intersection of complex analysis, symplectic geometry, and algebraic geometry (any smooth affine variety is a Stein manifold). New techniques in symplectic flexibility have given partial classification results of Stein manifolds up to analytic deformation. We present this result and a couple interesting consequences. We then discuss how overtwisted contact structures help us to extend the results to Stein cobordisms, and why these two perspectives are somewhat incompatible.