Gapless electronic topology driven by strong correlations is an emerging field, with heavy fermion compounds at its forefront. I will introduce the first such materials class, Weyl-Kondo semimetals [1–3], and report on the giant signatures of topology observed in Ce₃Bi₄Pd₃ [1,3] as well as the genuine topology control that can be achieved by magnetic-field tuning [4]. I will then discuss how symmetry considerations may help to identify new correlation-driven topological phases [5]. Finally, I will describe the discovery of an emergent topological phase that nucleates out of a strange-metal state [6] and discuss the potential of this new design principle for settings beyond heavy fermions [7]. [1] S. Dzsaber et al., Phys. Rev. Lett. 118, 246601 (2017). [2] H.-H. Lai et al., PNAS 115/1, 93 (2018). [3] S. Dzsaber et al., PNAS 118, e2013386118 (2021). [4] S. Dzsaber et al., Nat. Commun. 13, 5729 (2022). [5] L. Chen et al., Nat. Phys. 18, 1341 (2022). [6] D. M. Kirschbaum et al., arXiv2404.15924 (2024). [7] G. Checkelsky et al., Nat. Rev. Mater. 9, 509 (2024).