Holomorphic Floer theory is the analog of Floer theory for holomorphic symplectic manifolds. This topic has been recently explored, from several different perspectives, by Kontsevich-Soibelman and Doan-Rezchikov. In a different direction, I will in this talk present a conjectural picture relating holomorphic Floer theory of complex integrable systems to Donaldson-Thomas invariants. In physical terms, we will discuss a relation between the BPS spectrum of an N=2 4-dimensional field theory and the enumerative geometry of the corresponding Seiberg-Witten integrable system.