Stable homotopy in low dimensional topology

I will give a survey of stable homotopy refinements of Floer homology theories for 3-manifolds and Khovanov homology of knots and links. The emphasis will be on structural features of the theories that become more transparent from the stable homotopy perspective. I will also point out some open problems related to the functoriality with respect to 4-dimensional cobordisms in Seiberg-Witten theory.