Local to Global results in Floer theory from neck-stretching

Floer theoretic invariants have been a very powerful tool in symplectic geometry which involves `counting' pseudo-holomorphic curves. Obtaining local-to-global principles in Floer theory has remained quite hard because of dealing with moduli spaces of pseudoholomorphic curves. I will explain the heuristic of neck-stretching to obtain local-to-global results in Floer theory and review some recent successful applications of the heuristic.