Thermal Hall effect (THE) refers to the phenomenon whereby, in a magnetic field, when a longitudinal heat current flows through a material, the heat carriers are deflected, thereby generating a transverse temperature difference between the two lateral edges. The transition from electrical to thermal transport enables this effect to involve a wide range of carriers, thereby providing a unique perspective for investigating complex quantum states in condensed matter physics. THE is increasingly becoming a powerful probe of neutral excitations in materials and is used to explore multifield control phenomena in magneto-thermal-electrical coupled systems. Advances in the field of THE have significantly advanced the study of condensed matter systems under extreme conditions (low temperatures and strong magnetic fields) and have laid the groundwork for exploring novel magneto-thermal-electrical effects in quantum materials. This review systematically reviews recent theoretical and experimental progress on THE, with particular attention to the underlying heat carriers. Through an in-depth analysis of the transport mechanisms of different carriers, quantum material systems that can be used to investigate multicarrier coupled transport are identified, which will significantly facilitate the synergistic control of magneto-thermal-electrical transport in complex interacting systems. Finally, we propose a novel in situ, multiparameter integrated characterization method that enables simultaneous and precise measurement of magnetic, thermal, and electrical parameters on the same micro/nanoscale samples. This approach not only overcomes the limitations of bulk materials but also serves as a key experimental platform for revealing the mechanisms of multicarrier coupled transport in micro/nano samples.