Eremets’ discovery of high-Tc conventional superconductivity in H3S has profoundly reshaped superconductivity research.[1] In the last decade, superhydrides have pushed the limits of experimental and theoretical imagination, inaugurating a novel paradigm of cooperation between theory and experiment.[2] After superconducting Tc’s exceeding 200 K have been confirmed by different techniques in binary and ternary hydrides, the main challenge is to achieve reproducible control on the synthesis and pressure-quenching of metastable phases. [3] This shift is essential for moving hydride superconductivity toward accessible conditions and, eventually, practical use. In my talk I will highlight what I believe are the most promising directions and the main challenges connected to ab-initio modeling of compounds which should form, survive and operate under strongly non-ideal conditions. [4]

[1] A. P. Drozdov et al., Nature 525, 73 (2015) and ibid. 569, 528 (2019).

[2] J. A. Flores Livas, L.B., M. Eremets et al, Physics Reports 856, 1-78 (2020).

[3] R. Lucrezi, S. di Cataldo, W. von der Linden, L. Boeri and Christoph Heil, NPJ Computational Materials, 8, 119 (2022); S. di Cataldo, W. Von der Linden, L. Boeri, and ibid. 8, 2 (2022); S. Di Cataldo, C. Heil, W. von der Linden, and L. Boeri, Phys. Rev. B 104, L020511 (2021).

[4] S. di Cataldo, W. Cursio and L. Boeri, NPJ Comp. Mat. 12, 73 (2026); A. Cucciari and L. Boeri, Phys. Rev. X Energy, 5, 013006 (2026). L.E. Smith, P. Settembri, A. Cucciari, L. Boeri, G. Profeta and S. Hammes-Schiffer, PNAS 123 (21), e2605545123 (2026).