In heavy fermion compounds, the localized f-electron states hybridize with mobile conduction electrons, creating very narrow bands via the Kondo effect. Some of their most intriguing properties – from strange metallicity and unconventional superconductivity to correlation-driven topology – are more recently found in frustrated lattice and moiré flat band systems; whether Kondo physics underlies all these phenomena is a topic of intense interest [1]. The Weyl-Kondo semimetal state [2-4], first observed in the heavy fermion compound Ce3Bi4Pd3¬¬ [2,4], exhibits giant transport and thermodynamic signatures of topology, and can be genuinely tuned via the application of magnetic field [5]. In CeRu4Sn6, on the other hand, we discovered a topological semimetal phase that emerges from the material’s quantum critical state and displays a dome structure as a function of magnetic field and pressure [6]. This work has advanced a new design principle for correlation-driven topological phases, namely that a topological semimetal can emerge out of quantum criticality beyond the Landau quasiparticle picture. [1] J. G. Checkelsky et al., Nat. Rev. Mater. 9, 509 (2024) [2] S. Dzsaber et al., Phys. Rev. Lett. 118, 246601 (2017) [3] H.-H. Lai et al., Proc. Natl. Acad. Sci. U.S.A. 115, 93 (2018) [4] S. Dzsaber et al., Proc. Natl. Acad. Sci. U.S.A. 118, e2013386118 (2021) [5] S. Dzsaber et al., Nat. Commun. 13, 5729 (2022) [6] D. M. Kirschbaum et al., arXiv: 2404.15924