Quantum spin liquids (QSLs) represent exotic states of matter where quantum spins interact strongly yet evade long-range magnetic order down to absolute zero. Characterized by nonlocal quantum entanglement and the resultant fractionalized excitations, QSLs have emerged as a frontier in condensed matter physics, bolstered by the recent identification of several candidate materials. This field holds profound implications for understanding strong correlations, topological order, and emergent phenomena in quantum materials. Among them, the spin-$1/2$ Kitaev honeycomb model, featuring bond-directional Ising interactions, provides a rare exactly solvable QSL example. Its ground state is a topological QSL with spin degrees of freedom fractionalized into emergent Majorana fermions. Under an applied magnetic field, the Kitaev QSL transitions to a topologically nontrivial chiral spin liquid state with non-Abelian anyons, offering potential resources for topological quantum computation. The non-Abelian character of these anyons in the Kitaev QSL demonstrates a profound connection to certain topological superconductors and even-denominator fractional quantum Hall states. Since the theoretical prediction that the Kitaev model could manifest in spin-orbit-coupled materials such as honeycomb iridates and ruthenates, research has focused on identifying candidate compounds. In particular, experimental evidence suggests spin fractionalization and topological phenomena akin to the Kitaev model in the spin-orbit Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$. However, results and interpretations remain actively debated. This review begins with an exploration of QSLs in other systems, followed by a comprehensive survey of existing studies on Kitaev candidate materials, with a particular focus on $\alpha \text{−}{\mathrm{RuCl}}_3$. Rather than offering conclusive remarks, the review aims to inspire future research by examining several key aspects of the current literature and perspectives.

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• Anyons
• Frustrated magnetism
• Majorana fermions
• Quantum spin liquid
• Topological phases of matter
• Strongly correlated systems
• Kitaev model