The synthesis of MgB2-based materials under high pressure gave the possibility to suppress the evaporation of magnesium and to obtain near theoretically dense nanograined structures with high superconducting, thermal conducting, and mechanical characteristics: critical current densities of 1.8–1.0 × 106 A/cm2 in the selffield and 103 A/cm2 in a magnetic field of 8 T at 20 K, 5–3 × 105 A/cm2 in self-field at 30 K, the corresponding critical fields being Hc2 = 15 T at 22 K and irreversible fields Hirr = 13 T at 20 K, and Hirr = 3.5 T at 30 K, thermal conduction of 53 ±2 W/(m·K), the Vickers hardness HV = 10.12 ± 0.2 GPa under a load of 148.8 N and the fracture toughness K1C = 7.6 ± 2.0 MPa·m0.5 under the same load, the Young modulus E = 213 GPa. Estimation of quenching current and AC losses allowed the conclusion that high-pressure-prepared materials are promising for application in transformer-type fault current limiters working at 20–30 K.