Magnesium and its alloys are playing an increasingly important role in the transportation industry due to the pressing demand of lightweight structures to improve fuel efficiency and reduce CO2 emissions. But the shortcomings of poor room temperature (RT) formability and high temperature strength, tension–compression asymmetry, and anisotropy are among the major issues which are currently limiting their widespread applications. Recently, research and development activities of Mg–Zn–Y series alloys have significantly increased because of their superior mechanical properties arising from the formation of different ternary phases known as I (Mg3YZn6), W (Mg3Y2Zn3), and LPSO (Mg12YZn). In this review article, the crystal structure of these phases and their orientation relationships with hexagonal magnesium matrix are discussed. Recent advances about I, W, and LPSO phase containing Mg alloys are presented, along with the effects of these phases on the microstructural evolution and mechanical properties including tensile, compressive, fatigue, and creep resistance. Important aspects involving thermal stability, phase transformation, and influence of heat treatment are also described. Based on the current status, some existing issues are pointed out and further studies are suggested so as to warrant safe and reliable lightweight structural applications of Mg–Zn–Y alloys in the automotive industry.