Blue compact dwarf galaxies take up the low end of the distribution of metallicity as derived using collisional emission lines in ionized gaseous nebulae. In fact, the most metal poor objects in the Local Universe belong to this category. Nevertheless, the abundance discrepancy factor (ADF) found in some local HII regions whose metallicity have been derived by means of recombination lines and the offset claimed by some authors in relation to the predictions of some photoionization models question the real chemical status of these objects. In this contribution, we summarize the results of Pérez-Montero  (2010, MNRAS, 404, 2037) and we show how tailor-made models of a subsample of HII galaxies with a good determination of the thermal inner structure can be used to shed some light on this issue, helping also to study their star formation history and the properties of their ionizing stellar clusters.