The modern approach to the design of heat-resistant metal alloys (HRAs) is analyzed, according to which the creep rupture characteristics of an alloy are mostly determined by the strength of interatomic bonding at grain boundaries (GBs) and in the bulk of a matrix phase. The main attention is paid to the concept of “low alloying additions” to polycrystalline alloys with transition metals, because of which the cohesive strength of the GBs and the cohesion energy of the alloy matrix are increased. This approach is especially important in relation to alloys obtained by powder metallurgy, which, in the compacted state, are fine-grained polycrystals. The methodology for calculating the key parameters of the theory (the energy of impurity segregation to the grain boundaries Egb and to the free surface Efs, as well as the values of the partial molar energy of the cohesion of the alloys) from the first principles is given. The results of applying the theory to the study of Ni-, Cr- and Ti-based alloys and the development of new HRAs based on them are presented. Typical defects in the microstructures of objects obtained using additive technologies (AT) and the application efficiency of standard methods of processing powder alloys (Hot Isostatic Pressing (HIP), heat treatment (HT)) to improve the microstructure and increase the mechanical properties are considered.