Much has been learned over the past twenty years about the
global properties of symplectic manifolds (i.e., manifolds equipped
with a closed, nondegenerate two-form), with some of the most striking
results appearing in dimension four.  I'll give a brief general
overview of the subject, mentioning in particular how certain coarse
symplectic properties of a symplectic four-manifold, such as the
existence of certain spheres and the "symplectic Kodaira dimension,"
can tell us interesting things about the differential
topology of the manifold.   I'll then discuss some recent results
showing how these properties behave with respect to an important
surgery operation called the symplectic sum.  Time permitting, I'll end
with some interesting open questions.