Since their discovery in 1960(1), metallic glasses based on a wide range of elements have been developed(2). However, the theoretical prediction of glass-forming compositions is challenging and the discovery of alloys with specific properties has so far largely been the result of trial and error(3-8). Bulk metallic glasses can exhibit strength and elasticity surpassing those of conventional structural alloys(9-11), but the mechanical properties of these glasses are critically dependent on the glass transition temperature. At temperatures approaching the glass transition, bulk metallic glasses undergo plastic flow, resulting in a substantial decrease in quasi-static strength. Bulk metallic glasses with glass transition temperatures greater than 1,000 kelvin have been developed, but the supercooled liquid region (between the glass transition and the crystallization temperature) is narrow, resulting in very little thermoplastic formability, which limits their practical applicability. Here we report the design of iridium/nickel/tantalum metallic glasses (and others also containing boron) with a glass transition temperature of up to 1,162 kelvin and a supercooled liquid region of 136 kelvin that is wider than that of most existing metallic glasses(12). Our Ir-Ni-Ta-(B) glasses exhibit high strength at high temperatures compared to existing alloys: 3.7 gigapascals at 1,000 kelvin(9,13). Their glass-forming ability is characterized by a critical casting thickness of three millimetres, suggesting that small-scale components for applications at high temperatures or in harsh environments can readily be obtained by thermoplastic forming(14). To identify alloys of interest, we used a simplified combinatorial approach(6-8) harnessing a previously reported correlation between glass-forming ability and electrical resistivity(15-17). This method is non-destructive, allowing subsequent testing of a range of physical properties on the same library of samples. The practicality of our design and discovery approach, exemplified by the identification of high-strength, high-temperature bulk metallic glasses, bodes well for enabling the discovery of other glassy alloys with exciting properties.