The symplectic geography problem, originally posed by R. Gompf, ask which
ordered pairs of nonnegative integeres are realized as (chi(X), c1^2(X)) for some symplectic 4-manifold X. In this talk we address the geography problem of simply-connected spin and non-spin symplectic 4-manifolds in the regions with small Euler characteristic, with nonnegative signature or near the Bogomolov-Miyaoka-Yau line c1^2(X) = 9chi(X).