We report the density-functional-theory calculations of the exchange interactions and Curie temperature for a series of III-V and II-VI diluted magnetic semiconductors. We focus the discussion on the role of the holes in the establishing the ferromagnetic order in various systems. We suggest a method of the quantitative characterization of the properties of the holes. It is shown that there are two conflicting properties of the holes - delocalization from impurity and p-d interaction - whose combination determines the hole influence on the Curie temperature. We demonstrate that Hubbard U increases delocalization of the holes and decreases the strength of p-d interaction. Depending on the system these competing trends can lead to both increase and decrease of the Curie temperature. We show that high value of the Curie temperature for low impurity concentration is possible only in the case of substantial admixture of the impurity 3d states to hole states.