Topological materials, distinguished by their unconventional electronic band structures—featuring band inversions, topological crossings, and protected surface states—hold great potential for applications in advanced electronic devices. However, a key challenge lies in the fact that these topological features often occur at energies far from the Fermi level, limiting their impact on electronic transport. In this talk, I will demonstrate how strong electronic correlations, as exemplified by the Kondo effect, can drive the formation of topological bands near the Fermi level, with drastically enhanced electronic densities of states compared to the non-interacting case [1]. This results in giant, highly tunable topological transport signatures [2]. Finally, I will discuss strategies for expanding the material basis for these phenomena [3]. This work was supported by the Austrian Science Fund (I5868-FOR5249-QUAST, SFB-F86-Q-M&S, 10.55776/COE1), the European Research Council (ERC Advanced Grant 101055088), and the Air Force Office of Scientific Research (FA8655-24-1-7018). [1] S. Dzsaber et al., Phys. Rev. Lett. 118, 246601 (2017); H.-H. Lai et al., PNAS 115/1, 93 (2018). [2] S. Dzsaber et al., PNAS 118, e2013386118 (2021); S. Dzsaber et al., Nat. Commun. 13, 5729 (2022). [3] L. Chen et al., Nat. Phys. 18, 1341 (2022); G. Checkelsky et al., Nat. Rev. Mater. 9, 509 (2024); D. M. Kirschbaum et al., arXiv2404.15924 (2024).