We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. Contact 3-manifolds with distinct Kodaira dimensions behave differently when it comes to the geography of various kinds of symplectic fillings. On the other hand, we also prove that, given any contact 3-manifold, there is a lower bound of 2x+3σ for all of its minimal symplectic fillings. This is motivated by Stipsicz's result in  for Stein fillings. Finally, we discuss various aspects of exact self-cobordisms of fillable contact 3-manifolds.
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