Since Floer's work in 1988, various Floer homologies have been constructed for closed 3-manifolds, knots, and sutured manifolds.  In 2008, Kronheimer-Mrowka proposed a conjecture about isomorphisms among Floer homologies. In this talk, I will first introduce the history of the constructions in Floer theory and then introduce an approach to proving the isomorphisms. The idea is based on combinatorial version of Floer homology, which leads to an axiomatic construction of Floer homology. This work is joint with Baldwin, Li, Sivek, and Zemke.