The Weyl-Kondo semimetal (WKSM) state has recently been established experimentally and theoretically [1-3], and evidenced in the heavy fermion compound Ce3Bi4Pd3¬¬ [1,3]. In this state, transport and thermodynamic signatures of topology are strongly amplified, due to the flat dispersion inherent to heavy fermion materials and the pinning of Weyl nodes to the Fermi energy. Heavy fermion compounds are well known for their sensitivity to external control parameters such as magnetic field and pressure, providing exceptional playgrounds for testing the tunability and control of–a priori robust–topological phases. In this talk, I will present two such cases. In Ce3Bi4Pd3 we found that the application of relatively modest magnetic fields suppresses the topological signatures; we attribute this effect to the annihilation of Weyl nodes at a topological quantum phase transition [4]. CeRu4Sn6 has been suggested to be another topological semimetal [5,6]. Interestingly, inelastic neutron scattering experiments revealed that the material is quantum critical without tuning [7]. Our pressure- and magnetic field-tuning investigations reveal a dome-shaped WKSM phase, suggesting that this phase is stabilized by the quantum critical fluctuations [8]. References [1] S. Dzsaber et al., Phys. Rev. Lett. 118, 246601 (2017) [2] H.-H. Lai et al., Proc. Natl. Acad. Sci. U.S.A. 115, 93 (2018) [3] S. Dzsaber et al., Proc. Natl. Acad. Sci. U.S.A. 118, e2013386118 (2021) [4] S. Dzsaber et al., Nat. Commun. 13, 5729 (2022) [5] M. Sundermann et al., Sci Rep 5, 17937 (2016) [6] Y. Xu et al., Phys. Rev. X 7, 011027 (2017) [7] W. T. Fuhrman et al., Sci. Adv. 7, eabf9134 (2021) [8] D. M. Kirschbaum et al., in preparation