Magnesium-based bulk metallic glasses (BMG) have potential in applications ranging from biomedical to sports equipment and the Mg-Cu-Y system offers some of the most promising alloys. Phase relations and ternary solubility of the binary and ternary compounds of this system have been experimentally investigated. The Isothermal section of Mg-Cu-Y system at 673 K for the entire composition range has been constructed. Phase relations in the Cu-rich (>66 at.% Cu) region of the Mg-Cu-Y system has been determined for the first time. The homogeneity range of three ternary compounds has been determined. Solidifications behavior of several key alloys have been discussed based on the differential scanning calorimetry (DSC) experiments and thermodynamic calculations. Extensive analysis of the DSC curves has been carried out to relate them to the corresponding phase transformation reactions and temperatures. Some of the most promising metallic glass forming regions have been analyzed using thermodynamic calculations.