Abstract Quantum spin liquids(QSL) have fascinated physicists for nearly half a century since Anderson first introduced this concept with his resonating-valence-bond(RVB) idea in 1973. Although many progresses had been made, more challenges emerge from both theoretical and experimental perspectives. On the theory side, dealing with quantum mechanics acting on the spin system forces theorists to leave the comfort zone of semi-classical approaches. On the experimental side, high-quality QSL candidates remain very scarce, and the experimental results are often contradictory and inconclusive. In this thesis, I will present and discuss our thermal transport results on three different candidate materials with novel thermal conductivity and thermal Hall features that serve as crucial hallmarks for identifying and classifying the QSL materials. We introduce the theoretical frameworks for the antiferromagnetic(AFM) spin-1/2 Heisenberg system and Kitaev model. Transport theories of spin system, which are closely relevant to our results, are briefly discussed. After introducing the theoretical and experimental background, we report our discoveries on Na2BaCo(PO4)2, an AFM spin-1/2 system with geometry frustration of the triangular lattice. As thermal conductivity and Hall coefficients measured down to 0.3 K, we reveal a new gapless QSL state that exhibits unusual Hall effect in this charge-neutral system. Combining inelastic neutron scattering(INS) study, we confirm the observed QSL state hosts energy-continuous spin excitation, which is highly related to the theoretical prediction of spinon. The third and fourth chapters of this thesis are dedicated to BaCo2(AsO4)2 and α-RuCl3, which are promising candidates for realizing the Kitaev model. We report thermal conductivity and Hall coefficients of both materials measured down to 0.3 K. The observed thermal conductivity oscillations with novel angle dependence in α-RuCl3 strongly suggests a quantum oscillation mechanism that arises from the charge-neutral Fermi surface. Oscillatory behavior of thermal conductivity in BaCo2(AsO4)2 appears to be ’chaotic’ and remain unexplored theoretically. With the magnetic hysteresis carefully subtracted, we obtain the intrinsic thermal Hall effects of both materials and compare our results with other related works. We discuss the insights and limitations of our experiments, as well as future work.