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We introduce the Kodaira dimension of contact 3-manifolds and establish somebasic properties. In particular, contact 3-manifolds with distinct Kodariadimensions behave differently when it comes to the geography of various kindsof fillings. On the other hand, we also prove that, given any contact3-manifold, there is a lower bound of $2\chi+3\sigma$ for all its minimalsymplectic fillings. This is motivated by the bound of Stipsicz for Steinfillings. Finally, we discuss various aspects of exact self cobordisms offillable 3-manifolds.

The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings