This Review considers current Zr alloys and opportunities for advanced zirconium alloys to meet the demands of a structural material in fusion reactors. Zr based materials in the breeder blanket offer the potential to increase the tritium breeding ratio above that of Fe, Si and V based materials. Current commercial Zr alloys might be considered as a material in water-cooled breeder blanket designs, due to the similar operating temperature to fission power plants. For breeder blankets designed to operate at higher temperatures, current commercial Zr alloys will not meet the high temperature strength and thermal creep requirements. Hence, Zr alloys with an operational temperature capability beyond that of current commercial fission alloys have been reviewed, specifically: binary Zr alloy systems Zr-Al, Zr-Be, Zr-Cr, Zr-Nb Zr-Ti, Zr-Si, Zr-Sn, Zr-V and Zr-W; as well as higher order Zr alloys Zr-Mo-Ti, Zr-Nb-Ti, Zr-Ti-Al-V and Zr-Mo-Sn. It is concluded that, with further work, higher order Zr alloys could achieve the required high temperature strength, alongside ductility, while maintaining a low thermal neutron cross-section. However, there is limited data and uncertainty regarding the structural performance and microstructural stability of the majority of advanced Zr alloys for temperatures 500-700ºC, at which they would be expected to operate for helium- and liquid metal-cooled breeder blanket designs.