Extreme Emission Line Galaxies (EELGs) are characterized by their compact sizes and very high equivalent widths of certain optical emission lines (e.g. EW([OIII]) $>$ 500Å), indicative of very high specific star formation rates, similar to those detected in the reionization epoch galaxies. Many of them also present certain high-excitation emission-lines, such as {He II} at $\lambda$ 4686Å, indicative of a very hard incident stellar radiation. We compiled from the Sloan Digital Sky Survey (SDSS) the largest (around 2000) sample of EELGs using an automatic algorithm and we studied their physical properties and chemical abundances from the direct method. This allowed us to study the fundamental relations followed by this type of galaxies (e.g MZR, O/H vs N/O). This observational feedback can be used to constrain photoionization models from which we can provide model-based solutions to derive the properties of the high-redshift galaxies using only their available observed strong emission-lines. Among the model-based solutions that benefit from this constrains and can be subsequently applied to high-redshift EELGs it is the HII-CHI-mistry code. We show that this code can be adapted to give specific solutions to derive e.g. chemical abundances and to interpret the softness diagram involving the nebular He II emission. The latter can be used to quantify the hardness of ionizing incident spectral energy distribution and the fraction of leaking photons.