The ability to control topological states at will holds great promise for its application in topological quantum devices. Heavy fermion compounds are well known for their excellent tunability, and provide an exceptional platform to explore the intersection of strong electronic correlations and electronic topology [1]. In this talk, I will focus on tuning experiments performed on heavy fermion semimetals in which Weyl nodes form in a setting of broken inversion and preserved time-reversal symmetries. In Ce₃Bi₄Pd₃, which exemplifies the notion of Weyl-Kondo semimetal (WKSM) [2,3], and in which a giant spontaneous Hall effect has been observed [4], 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 [5]. CeRu₄Sn₆ is another WKSM candidate material [6]. Interestingly, inelastic neutron scattering experiments revealed that the material is quantum critical without tuning [7]. I will present pressure-tuning investigations of CeRu4Sn6, and discuss whether the WKSM state may nucleate out of quantum critical fluctuations [8].