Abstract: The Kitaev model is a spin-1/2 model for a quantum spin liquid defined on a twodimensional honeycomb lattice. It is an exactly solvable model, with topological order, fractionalized Majorana fermions and a Z₂ gauge field, which provides a new direction for the study of topological physics, nonvolatile storage technology, and topological quantum computation. Different from the quantum spin liquid state induced by geometrical frustration in triangular and kagomé lattices, the Kitaev quantum spin liquid is a consequence of the bond-dependent anisotropic Kitaev interactions. In recent years, searching for such interactions in real materials has become a new route to realize quantum spin liquids. Among the candidate materials, α-RuCl₃, a Mott insulator with a honeycomb lattice, is believed to be the most promising. In this article we present the progress of experimental studies on Kitaev quantum spin liquids in recent years, with a focus on α-RuCl₃. In particular, neutron scattering studies of the spin dynamics relevant to the Kitaev quantum spin liquid model will be highlighted.