Correspondence theorems mean to give correspondence between tropical curves and holomorphic curves. For so-called non-superabundant tropical curves, essentially these theorems were already settled. There, the automatic vanishing of the obstructions was crucial. On the other hand, for superabundant tropical curves, such vanishing does not hold, and new ideas are required. In this talk, first we give an effective combinatorial description of the superabundant tropical curves, and based on it, we give correspondence theorems for these curves.