A Stein manifold is a complex manifold admitting a proper holomorphic embedding into C^n. Work of Cieliebak-Eliashberg (among others) fundamentally relates the geometry of Stein manifolds to their symplectic structures. This relationship gives rise to Weinstein handle decompositions, which allows us to study Stein manifolds via Legendrian knot theory in contact manifolds. This gives rise to new tools: the h-principles in contact geometry. We'll explain the motivation behind contact geometry, what the h-principle is, and how those topics tie together to influence the geometry of Stein manifolds, and cobordisms.