When taking into account the electronic correlations such as the onsite Coulomb repulsion and coupling between electrons, spins and orbitals, many fascinating novel quantum states beyond the free-electron framework can emerge, e.g., unconventional superconductiviity and quantum spin liquids. The understanding of these new states not only will expand the existing territory of our knowledge, but also likely lead to revolution in quantum science and technology. Therefore, studying the strongly correlated physics is a cutting-edge theme in condensed matter physics. The parent state of cuprate high-temperature superconductors is a Mott insulator, an insulating state due to the strong electronic correlation, whereas the band theory predicts it to be metallic. Due to the Coulomb gap in Mott insulators, the charge degree of freedom is often frozen, which makes electrical transport measurements inapplicable. As a probe sensitive to the elementary excitations of quasiparticles not limited to electrons, but also including magnons, spinons, as well as phonons, thermal transport measurements play an important role in the study of strongly correlated electronic systems. In this paper, we review some of the recent interesting results on unconventional superconductors, heavy fermions and quantum spin liquids utilizing the longitudinal thermal transport measurements, complimentary to our recent review article on the progress of the transverse thermal conductivity measurements on the thermal Hall effect.
