Quantum spin liquid is a novel magnetic state without long-range order even at zero temperature due to strong quantum fluctuations. The ground state of quantum spin liquid cannot be described by order parameters, and there is no symmetry breaking in this exotic state, which means that the realization of quantum spin liquid states will break through the paradigm of Landau’s theory. Studies on quantum spin liquid will be helpful for the understanding of the mechanism of high-temperature superconductivity and the application of quantum calculation and quantum information. Although there are many advances in the theory, no material is confirmed to be a real quantum spin liquid so far, making it important to realize a quantum spin liquid material and confirm its properties. Muon spin relaxation, a powerful technique that is extremely sensitive to magnetic fields, has been widely used in the study of quantum spin liquid candidates. Muon spin relaxation can observe whether there is long-range order in the ground state, and measure the fluctuation rate in the system, both of which are the basic properties of quantum spin liquid. This article gives a brief introduction to the quantum spin liquid state and muon spin relaxation technique. Then recent experimental works, especially muon spin relaxation experiments, on different systems, including one-dimensional antiferromagnetic Heisenberg chain (copper benzoate), triangular lattice (YbMgGaO4, NaYbO2 and TbInO3), kagomè lattice [ZnCu3(OH)6Cl2 and Tm3Sb3Zn2O14], honeycomb lattice (Na2IrO3 and α-RuCl3) and pyrochlore lattice (Tb2Ti2O7, Pr2Ir2O7 and
Ce2Zr2O7) are reviewed.
