Quantum spin liquids (QSLs) are exotic quantum many-body states in frustrated magnets that evade conventional magnetic order down to absolute zero temperature, featuring long-range quantum entanglement, fractionalized excitations, and emergent gauge structures. The triangular lattice serves as a canonical platform for studying QSLs; however, the simplest spin-1/2 nearest-neighbor Heisenberg triangular-lattice antiferromagnet possesses a 120^\circ Néel ordered ground state rather than a spin liquid. Realizing QSLs in real triangular-lattice materials therefore relies on additional mechanisms such as next-nearest-neighbor exchange, XXZ exchange anisotropy, and bond-dependent anisotropic interactions induced by strong spin-orbit coupling. This article reviews the theoretical foundations, candidate materials, and recent experimental progress on rare-earth triangular-lattice QSLs, with a focus on Yb³⁺-based compounds whose effective pseudospin-1/2 description and high-quality single-crystal availability make them the most extensively studied systems to date. We first examine YbMgGaO₄, where inelastic neutron scattering revealed broad continuum excitations suggestive of fractionalization, but Mg²⁺/Ga³⁺ site disorder and spin-glass-like behavior in the sister compound YbZnGaO₄ have cast doubt on its intrinsic QSL candidacy. We then turn to the \rmNaYbCh_2 (Ch = O, S, Se) family, which eliminates such mixed-valence disorder at the structural level. Thermodynamic and local-probe measurements consistently show the absence of long-range order and spin freezing; single-crystal inelastic neutron scattering on NaYbSe₂ has identified spinon-type continuum excitations in a structurally clean setting. The chemical substitution O→S→Se provides a clean tuning pathway across different exchange regimes. Comparisons with magnetically ordered analogues KYbO₂, KYbSe₂, and CsYbSe₂ through spin-wave fitting supply quantitative constraints on the effective Hamiltonians. Current evidence indicates that the \rmNaYbCh_2 family represents one of the most promising rare-earth triangular-lattice QSL candidate platforms to date.