While calcium ferrite slags have been successfully used in continuous copper converting for the last 30 years, ferrous calcium silicate slag was proposed about 8 years ago as an additional alternative for copper smelting. Although both slags are normal extensions of each other their phase relations have not been completely clarified. In this paper the liquidus relations of both slags have been quantified at various areas that cover both of them. The existing experimental data have been first reviewed and discussed in relation to the solidification procedure. An original physical model is then used to predict various diagrams of the liquidus surface of both slags. It is shown that the ternary liquidus diagrams normally used for FeOx-SiO2-CaO system are not suitable for industrial slags. The new model diagrams of Fe/CaO versus SiC2 and Fe/SiO2 versus CaO as well as Fe/CaO versus Temperature and Fe/SiO2 versus temperature are proven to be much more convenient for ferrite and ferrous calcium silicate slags. Based on these diagrams the effect of SiO2 and CaO on the melting temperature is quantified. The effect of Cu2O is also quantified through the model. Some Fe/CaO versus Cu2O and Fe/SiO2 versus CaO at various copper contents are predicted and the results show good agreement with the experimental data. It is also shown that in the presence of liquid copper, Cu2U is dissolved in the slag depending on the oxidation degree of the system and might lower the liquidus temperature. Some discussions are also presented taking into account plant observations and important conclusions are drawn for copper smelting and converting.