It is known that every smooth oriented closed 4-manifold with b+> 0 admits a near-symplectic structure, i.e a closed 2-form which vanishes in a particular way along a link and is non-degenerate on the complement. Motivated by Taubes’ programme of constructing smooth invariants via pseudo-holomorphiccurve counting in near-symplectic 4-manifolds, this subject recently became a big deal of interest among 4-manifold topologists. D. Gay and R. Kirby gave an explicit construction of these manifolds by using symplectic and contact surgery techniques, and D. Auroux, S. Donaldson and L. Katzarkov showed that these forms are supported by singular Lefschetz fibrations. This talk is a survey of these constructions, and certain follow-up ideas.