I'll explain how pseudoholomorphic curves can be combined 
with several other techniques to give simple necessary and sufficient 
conditions for a symplectic four-manifold arising as a symplectic sum 
along surfaces of positive genus to be minimal, or to have nonpositive 
Kodaira dimension.  Among other things, this gives a new way of showing 
that certain small four-manifolds are exotic, and proves a conjecture 
of Stipsicz about the minimality of fiber sums of Lefschetz fibrations.